Directly grown III-V quantum dot (QD) laser on on-axis Si (001) is a good candidate for achieving monolithically integrated Si photonics light source. Nowadays, laser structures containing high quality InAs / GaAs QD are generally grown by molecular beam epitaxy (MBE). However, the buffer layer between the on-axis Si (001) substrate and the laser structure are usually grown by metal-organic chemical vapor deposition (MOCVD). In this paper, we demonstrate all MBE grown high-quality InAs/GaAs QD lasers on on-axis Si (001) substrates without using patterning and intermediate layers of foreign material.