We investigate the equiform-Bishop Hasimoto surfaces ℘(\sigma, t) in Minkowski 3-space in this paper. In E^3_1, in different three cases, the geometric properties of equiform-Bishop Hasimoto surfaces are discussed. For each case, the equiformBishop Gaussian and mean curvatures of the equiform-Bishop Hasimoto surface are determined. Then, in E^3_1, we characterize the parameter equiform Bishop curves of equiform-Bishop Hasimoto surfaces.