This paper presents a least-pth approach to the optimal design of 2-D FIR digital filters in the minimax sense. Features of the proposed approach include: it does not need to adapt the weighting function involved and no constraints are imposed during the course of optimization. More important, the algorithm enjoys global convergence to the minimax design regardless of the initial design used. This property is an immediate consequence of the fact that for each even power p, the weighted Lp objective function is convex in the entire parameter space. Two minimax designs of 2-D FIR filter with low passband group delay are included to illustrate the proposed method.