New procedure of designing slotted photonic crystal waveguides (SPCW) is proposed to achieve slow light with improved normalized delay-bandwidth product (NDBP) and low group velocity dispersion, which is suitable for both the W1 defect mode and the slot mode. The lateral symmetry of the waveguide in our study is broken by shifting the air holes periodically along the slot axis . The conversion of the “flat band” from band-up slow light to band-down slow light is achieved for W1 defect mode. The group index curves of W1 mode change from U-like to step-like and the group index of 47, 67 and 130 are obtained with the bandwidth over 7.2, 4.8, and 2.3nm around 1550nm, respectively. We also obtain the group index of 42, 55, and 108 for the slot mode with the bandwidth over 6.2, 5.6, and 2.2nm. Then the low dispersion slow light propagation is numerically demonstrated by the finite-difference time-domain method.