In late 1994, ahead of the start of the next season, he was signed by Åge Hareide, manager of the first-tier club Molde, for a fee of NOK200,000. On 22 April 1995, Solskjær made his debut for Molde against Brann, scoring twice in a 6–0 victory. In his second game on 29 April, Solskjær scored a hat-trick helping Molde 5–4 win over Viking. On 14 May, he scored another brace in a 2–1 win over Hamarkameratene. Two days later, he netted a hat-trick as Molde thrashed Hødd 7–2. Solskjær scored a penalty in Molde's 4–1 victory over Strindheim on 30 July.