We wish to construct solutions of Taub-NUT spacetime in Einstein-Born-Infeld gravity in even dimensions. Since the Born-Infeld theory is a nonlinear electrodynamics theory, in leads to nonlinear differential equations. However, a proper analytical solution was not obtained, we try to solve it numerically (by the Runge-Kutta method) with initial conditions coinciding with those of our previous work in Einstein-Maxwell gravity. We solve the equations for 4, 6 and 8 dimensions and do data fitting by the least-squares method. For N = l = b = 1, the metric turns to the NUT solution only in 8 dimensions, but in 4 and 6 dimensions the spacetime does not have any NUT solution.