We report the first demonstration of direct modulation of InAs/GaAs quantum dot (QD) lasers grown on on-axis (001) Si substrate. A low threading dislocation density GaAs buffer layer enables us to grow a high quality 5-layered QD active region on on-axis Si substrate. The active layer has p-modulation doped GaAs barrier layers with a hole concentration of 5 × 1017 cm-3to suppress gain saturation. Small-signal measurement on a 3 × 580 μm2 Fabry-Perot laser showed a 3dB bandwidth of 6.5 GHz at a bias current of 116 mA. A 12.5 Gbit/s non-return-to-zero signal modulation was achieved by directly probing the chip. Open eyes with an extinction ration of 3.3dB was observed at room temperature. The bit-error-rate (BER) curve showed no error-floor up to BER of 1 × 10-13. 12 km single-mode fiber transmission experiments using the QD laser on Si showed a low power penalty of 1 dB at 5Gbit/s. These results demonstrate the potential for QD lasers epitaxially grown on Si to be used as a low-cost light source for optical communication systems.