1 and 1 Existence and uniqueness of the solution to the Lp Minkowski problem for the electrostatic $\wp$-capacity are proved when p > 1 and 1 < $\wp$ < n. These results are nonlinear extensions of the solution to the Lp Minkowski problem for $\wp$-capacity when p = 1 and 1 < $\wp$ < n by Colesanti et al. and Akman et al., and the classical solution to the Minkowski problem for electrostatic capacity when p = 1 and $\wp$ = 2 by Jerison.