In order to obtain a fast multiplication on elliptic curves, the Gallant-Lambert-Vanstone(GLV) method is introduced to the general situation in dimension 4, one of the open problems in Galbraith, Lin and Scott's work(J. Cryptol. DOI: 10.1007/s00145-010-9065-y) is answered, that is, studying the performance of 4-dimensional GLV method for faster point multiplication on some GLS curves over Fp² with j-invariant 1728. Finally some results and examples are presented, showing that the 4-dimensional GLV method runs in between 70% and 73% the time of the 2-dimensional GLV method which Galbraith et al. did in their work.