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In the multi-target scenarios, we consider the problem of constant false alarm rate (CFAR) target detection. For the conventional CFAR algorithms, the multi-target detection performance is mainly limited by the interference target tolerance within the reference window. In this paper, we propose a local ordered statistic CFAR (OS-CFAR) target detector based on compressed sensing (CS) radar system to address the degradation of detection performance in multi-target scenarios. With the analog-information-converter (AIC), the radar intermediate frequency (IF) signal is compressively sampled into discrete linear measurements. At each detection stage, multiple signal components are generated by correlation tests between the sensing matrix and linear measurements. By support set merge and proxy pruning, the signal components with the largest energy are retained. These components are the echoes reflected from the targets. Since target components are output in decreasing order of correlation, the proposed detector only requires a local OS-CFAR decision in the interval where the least correlated target is located, rather than traversing the entire interval. By continuously updating the detection stage, all targets that satisfy the false alarm rate requirement can be screened out. Finally, the performance of the proposed detector in the multi-target scenarios is confirmed by simulation results. [ABSTRACT FROM AUTHOR]