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In the frequency modulated continuous wave radar systems, when the transmitter uses periodic linear symmetric triangular wave modulation, the received signal after processed by the mixer will have many harmonics. In the single target detection, this effect can be ignored. However, in the multi-target detection, targets with different ranges and velocities lead to overlapping of the harmonics. Using the peak detection method at the receiver can only detect the maximum peak position, so the information contained in the other peaks is concealed. In order to resolve this issue, we propose to use an antenna array receiver with array signal processing. This not only improves the signal-to-noise ratio but also resolves successfully the multi-target detection problem.