Human activity recognition (HAR) by using wearable accelerometers has gained significant interest in recent years in a range of healthcare areas, including inferring metabolic energy expenditure, predicting falls, measuring gait parameters and monitoring daily activities. The implementation of HAR relies heavily on the correctness of sensor fixation. The installation errors of wearable accelerometers may dramatically decrease the accuracy of HAR. In this paper, a method is proposed to improve the robustness of HAR to the installation errors of accelerometers. The method first calculates a transformation matrix by using Gram-Schmidt orthonormalization in order to eliminate the sensor's orientation error and then employs a low-pass filter with a cut-off frequency of 10 Hz to eliminate the main effect of the sensor's misplacement. The experimental results showed that the proposed method obtained a satisfactory performance for HAR. The average accuracy rate from ten subjects was 95.1% when there were no installation errors, and was 91.9% when installation errors were involved in wearable accelerometers.