In this paper, a low power and fast DCT (Discrete Cosine Transform) using multiplier-less method is presented with a new modified FGA (Flow-Graph Algorithm), which is derived from our previously presented FGA of DCT based on Loeffler algorithm. The multiplier-less method is based on the replacement of multiplications with a minimum number of additions and shifts. The proposed FGA is performed and compared to a previous one. The results of FPGA implementations on Altera Cyclone II show the increase of the maximum frequency, the decrease of the resources usage and the reduction of the dynamic power by 7.2 % at 120 MHz of clock frequency with a new proposed FGA algorithm. Another comparison with recent published results has been done and proves the efficiency of the proposed FGA.