The directional accuracy of the rate-bias laser inertial measurement unit(IMU) is not only related to the laser gyroscope but also has a great relationship with the accelerometer. Therefore, the study of the index system of accelerometer is of great significance to improve the performance and accuracy of the rate-bias laser IMU. This paper analyzes the influence of accelerometer on directional accuracy from the initial alignment and direction hold. The zero deviation error and random walk of accelerometers will lead to the error of initial alignment heading angle. In order to obtain high precision heading keeping accuracy, the drift trend of the three accelerometers needs to be consistent. The experimental results show that the bias stability of the accelerometer is increased by 4 times, and the statistical accuracy of the initial alignment heading angle is improved by 30%. Under the same accuracy of accelerometer, the heading keeping accuracy of the rate-bias laser IMU with the same accelerometer drift trend have a 57% improvement than that of the rate-bias laser IMU with the inconsistent accelerometer drift trend.