The laser interferometer is one of the most important key technologies for the space gravitational wave detection. A laser interferometer prototype with pico-meter measurement precision for Taiji mission in China is presented in the paper. The results showed that the path-length measurement precision reached 5 pm/√Hz within the frequency range of 10 mHz – 1 Hz by improving the temperature fluctuation noise and electronic readout noise of the laser interferometer, which meets the requirement of Taiji Pathfinder mission inside the frequency range of 1 mHz – 1 Hz under the weak-light condition. It would be a fine experimental platform for the key technologies demonstration including the laser pointing modulation and the laser phase-locking control to improve the precision for the low measurement noise.