The electronic structures of phosphorene-like SnS/SnSe nanoribbons and the transport properties of a SnS-SnSe nanoribbon lateral heterostructure are investigated by using first-principles calculations combined with nonequilibrium Green's function (NEGF) theory. It is demonstrated that SnS and SnSe nanoribbons with armchair edges (A-SnSNRs and A-SnSeNRs) are semiconductors, independent of the width of the ribbon. Their bandgaps have an indirect-to-direct transition, which varies with the ribbon width. In contrast, Z-SnSNRs and Z-SnSeNRs are metals. The transmission gap of armchair SnSNR-SnSeNR is different from the potential barrier of SnSNR and SnSeNR. The I-V curves of zigzag SnSNR-SnSeNR exhibit a negative differential resistive (NDR) effect due to the bias-dependent transmission in the voltage window and are independent of the ribbon width. However, for armchair SnSNR-SnSeNR, which has a low current under low biases, it is only about 10-6 μA. All the results suggest that phosphorene-like MX (M = Sn/Ge, X = S/Se) materials are promising candidates for next-generation nanodevices.