The invention relates to a method and a system for determining magnetotelluric time domain impedance. By equivalently solving the optimization problem, the operation of matrix inversion is avoided, and meanwhile, the noise type and distribution in the signal are not assumed, so that the influence of peak impulse noise is suppressed without Bayesian estimation, the impedance estimation process is simplified, and the calculated amount is reduced; moreover, by using an interleaved multiplier iteration method, the updating of iteration parameters can be accelerated, the number of variables of eachiteration can be reduced, and the convergence speed is faster than the steepest descent iteration used by the traditional method; and besides, time domain impedance estimation is converted into an unconstrained convex optimization problem by adopting an improved algorithm, and the convex optimization problem is solved to obtain a global optimal value, so that the problem that the steepest descentiteration of local optimization is caught in a local minimum value in a traditional method is avoided, fitting errors are reduced, and a convergence result is more reliable.