The development of an origin–destination (OD) demand matrix is crucial for transit planning. With the help of automated data, it is possible to estimate a stop-level OD matrix. We propose a novel method for estimating transit route OD matrix using automatic passenger count (APC) data. The method uses (Formula presented.) norm regularizer, which leverages the sparsity in the actual OD matrix. The technique is popularly known as compressed sensing (CS). We also discuss the mathematical properties of the proposed optimization program and the complexity of solving it. We used simulation to assess the accuracy and efficiency of the method and found that the proposed method is able to recover the actual matrix within small errors. With increased sparsity in the actual OD matrix, the solution gets closer to the actual value of the matrix. The method was found to perform more efficiently even for different demand patterns. We also present a real numerical example of OD estimation of the A Line Bus Rapid Transit (BRT) route in Twin Cities, MN.