theory in higher dimensional spacetimes, in which contains most of Einstein assumptions, is Lovelock gravity [@Lovelock]. Lovelock gravity field equation contains metric derivatives no higher second order and therefore its quantization is free of ghost [@GhostFree]. Since the higher curvature terms of Lovelock Lagrangian appear in the low-energy limit of string theory, black hole solutions of Lovelock gravity have been attracting renewed interest. The action of Lovelock gravity in a compressed form can be written as $$I_{G}=\int d^{d}x\sqrt{-g}\sum\limits_{k=0}^{d/2}\alpha _{k}\pounds _{k},
\label{LovelockAction}$$ where $\alpha_{k}$’s are arbitrary constants and $\pounds _{k}$’s are the Euler densities of the $2k$-dimensional manifolds with the following explicit form $$\pounds _{k}=\delta _{\rho _{1}\sigma _{1}...\rho _{k}\sigma _{k}}^{\mu
_{1}\nu _{1}...\mu _{k}\nu _{k}}R_{\mu _{1}\nu _{1}}^{\rho _{1}\sigma
_{1}}...R_{\mu _{k}\nu _{k}}^{\rho _{k}\sigma _{k}}.  \label{Lk}$$In Eq. (\[Lk\]), $\delta _{\rho _{1}\sigma _{1}...\rho _{k}\sigma
_{k}}^{\mu _{1}\nu _{1}...\mu _{k}\nu _{k}}$ and $R_{\mu \nu }^{\rho \sigma
} $ are, respectively, the generalized totally anti-symmetric Kronecker delta and the Riemann tensor.

The objective of this paper is to find topological (asymptotically adS) black hole solutions of third order Lovelock gravity in the presence of two classes of Born-Infeld (BI) type nonlinear electrodynamics (NED). Some black object solutions of third order Lovelock theory coupled with NED have been studied 