We propose a weighted least-squares (WLS) design method for multi-dimensional (M-D) complex-coefficient finite-extent impulse response (FIR) filters. We consider the general form of M-D FIR filters having arbitrary frequency responses and low group delays. We formulate the proposed WLS design as a second-order cone programming problem. Design examples confirm that the proposed method provides the state-of-the-art M-D FIR filter designs with almost constant group delay.