user-1: The Marshall defence goes 1. d4 d5 2. c4 Nf6?!
I played this game recently as white. It was the first time I saw the Marshall in a game and the real contest was over by move 14.
[FEN ""]
[StartPly "7"]

1. d4 d5 2. c4 Nf6 3. cxd5 Nxd5 4. Nf3 Bg4 5. e4 Nb6 6. Be2 Bxf3 7. Bxf3 e6 8. O-O Be7 9. d5 O-O 10. dxe6 fxe6 11. Qb3 Qd7 12. Bg4 Rf6 13. Rd1 Bd6 14. e5 Rg6 15. exd6 Rxg4 16. dxc7 Rd4 17. Rxd4 Qxd4 18. Qxe6+ Kf8 19. c8=R+ Nxc8 20. Qxc8+ Ke7 21. Qxb7+ Kf6 22. Qf3+ Ke6 23. Qe3+ Qe5 24. Nc3 Nc6 25. f4 Qxe3+ 26. Bxe3 a5 27. Rd1 Ne7 28. Nb5 Rb8 29. a4 Nd5 30. g4 Nxe3 31. Re1 Rf8 32. Rxe3+ Kd7 33. f5 g6 34. Rf3 Kc6 35. Kg2 gxf5 36. Rxf5 Rg8 37. Kf3 Rd8 38. Kg3 Rd3+ 39. Rf3 Rd2 40. b3 Rb2 41. Na3 Ra2 42. Nc4  1-0

Now the Marshall defence is considered to be dubious, even refuted: 

This [1. d4 d5 2. c4 Nf6?! 3. cxd5 Nxd5 4. Nf3!] is considered to be the refutation for this defence

Source: GreenCastleBlock on YouTube, @ 0:58.
But my question is there any move after 4. Nf3 where black gains equality?

user12873: The Marshall is considered dubious since Black essentially just gives up full control over the center.  For that reason, there is no move that would give Black absolute equality after 4. Nf3
There are probably good development schemes that would give Black a playable game, but there is no direct path to absolute equality.  Heck, there's no direct path to complete equality for Black in even the most respected openings, such as the Grunfeld and Slav.  Even in those openings Black has to work to achieve an equal game.
The best development scheme that I know of in the Marshall is the following (after 4. Nf3):
g6, Bg7, 0-0, Nc6, Bg4.  And if White plays e4 at any point, the Knight on d5 retreats to b6.  This gives Black a reasonable game, and I believe it is the most popular system in the reference database.  But even here, White keeps a comfortable edge.

-1: <p>The Marshall defence goes <strong>1. d4 d5 2. c4 Nf6?!</strong></p>

<p>I played this game recently as white. It was the first time I saw the Marshall in a game and the real contest was over by move 14.</p>

<pre><code>[FEN ""]
[StartPly "7"]

1. d4 d5 2. c4 Nf6 3. cxd5 Nxd5 4. Nf3 Bg4 5. e4 Nb6 6. Be2 Bxf3 7. Bxf3 e6 8. O-O Be7 9. d5 O-O 10. dxe6 fxe6 11. Qb3 Qd7 12. Bg4 Rf6 13. Rd1 Bd6 14. e5 Rg6 15. exd6 Rxg4 16. dxc7 Rd4 17. Rxd4 Qxd4 18. Qxe6+ Kf8 19. c8=R+ Nxc8 20. Qxc8+ Ke7 21. Qxb7+ Kf6 22. Qf3+ Ke6 23. Qe3+ Qe5 24. Nc3 Nc6 25. f4 Qxe3+ 26. Bxe3 a5 27. Rd1 Ne7 28. Nb5 Rb8 29. a4 Nd5 30. g4 Nxe3 31. Re1 Rf8 32. Rxe3+ Kd7 33. f5 g6 34. Rf3 Kc6 35. Kg2 gxf5 36. Rxf5 Rg8 37. Kf3 Rd8 38. Kg3 Rd3+ 39. Rf3 Rd2 40. b3 Rb2 41. Na3 Ra2 42. Nc4  1-0
</code></pre>

<p>Now the Marshall defence is considered to be dubious, even refuted: </p>

<blockquote>
  <p>This [1. d4 d5 2. c4 Nf6?! 3. cxd5 Nxd5 4. Nf3!] is considered to be the refutation for this defence</p>
</blockquote>

<p>Source: <a href="https://www.youtube.com/watch?v=2urOgXfleco&amp;t=117s" rel="nofollow noreferrer">GreenCastleBlock on YouTube</a>, @ 0:58.</p>

<p>But my question is <strong>there any move after 4. Nf3 where black gains equality?</strong></p>
 12873: <p>The Marshall is considered dubious since Black essentially just gives up full control over the center.  For that reason, there is no move that would give Black absolute equality after 4. Nf3</p>

<p>There are probably good development schemes that would give Black a playable game, but there is no direct path to absolute equality.  Heck, there's no direct path to complete equality for Black in even the most respected openings, such as the Grunfeld and Slav.  Even in those openings Black has to work to achieve an equal game.</p>

<p>The best development scheme that I know of in the Marshall is the following (after 4. Nf3):</p>

<p>g6, Bg7, 0-0, Nc6, Bg4.  And if White plays e4 at any point, the Knight on d5 retreats to b6.  This gives Black a reasonable game, and I believe it is the most popular system in the reference database.  But even here, White keeps a comfortable edge.</p>
