In cubic lattice model, we have devised a new move set that is fast and suitable for use in a protein folding study by Monte-Carlo simulations, where the number of moving monomers are more extended and flexible in pivot moves and crankshaft moves. In Monte Carlo simulations using 100 model proteins with 27-mers in a cubic lattice, this new move set shows much higher foldicity and faster mean first passage time than the most commonly used move set. From the results of lattice simulation at equilibrium conditions, it is found that the conformational space sampled by this new move set is almost the same as the one sampled with the commonly used move set. However, in the simulation at low temperature, the detailed kinetic folding paths of this new move set are shown to be different from that of the commonly used move set.