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Background The compressed sensing (CS) of acceleration data has been drawing increasing attention in gait telemonitoring application. In such application, there still exist some challenging issues including high energy consumption of body-worn device for acceleration data acquisition and the poor reconstruction performance due to nonsparsity of acceleration data. Thus, the novel scheme of compressive sensing of acceleration data is needed urgently for solutions that are found to these issues. Methods In our scheme, the sparse binary matrix is firstly designed as an optimal measurement matrix only containing a smallest number of nonzero entries. And then the block sparse Bayesian learning (BSBL) algorithm is introduced to reconstruct acceleration data with high fidelity by exploiting block sparsity. Finally, some commonly used gait classification models such as multilayer perceptron (MLP), support vector machine (SVM) and KStar are applied to further validate the feasibility of our scheme for gait telemonitoring application. Results The acceleration data were selected from open Human Activity Dataset of Southern California University (USC-HAD). The optimal sparse binary matrix (a smallest number of nonzero entries is 8) is as strong as the full optimal measurement matrix such as Gaussian random matrix. Moreover, BSBL algorithm significantly outperforms existing conventional CS reconstruction algorithms, and reaches the maximal signal-to-noise ratio value (70 dB). In comparison, MLP is best for gait classification, and it can classify upstairs and downstairs patterns with best accuracy of 95 % and seven gait patterns with maximal accuracy of 92 %, respectively. Conclusions These results show that sparse binary matrix and BSBL algorithm are feasibly applied in compressive sensing of acceleration data to achieve the perfect compression and reconstruction performance, which has a great potential for gait telemonitoring application.