Compressed sensing (CS) has attracted a lot of research interests in data transmission, since it can significantly reduce the redundancy of the data while still holding the information completely. Generally, in order to deal with the experienced time-varying channel, the data transmission scheme based on CS needs to estimate the channel frequently. In this paper, we propose a novel CS-based data transmission scheme for slowly time-varying channel, which estimates channel and reconstructs data jointly. Specifically, the scheme consists of a data reconstruction part and a channel state information (CSI) update part. The former reconstructs the data with inaccurate CSI by modeling the problem as a perturbed CS reconstruction problem. The latter updates the CSI with the reconstruction result as a semi-blind channel estimation problem. Comparing with the classical scheme, the proposed one enjoys a reduced cost by avoiding inserting pilots into data frame frequently. Simulation results demonstrate that our proposed scheme works robustly in slowly time-varying channel and the performance is comparable to that of the scheme reconstructing the data with perfect CSI.