The performance of an partial relay selection on the decode-and-forward (DF) mode cognitive radio (CR) relay networks is studied, with some important factors, including the outage probability, the bit error ratio (BER), and the average channel capacity being analyzed. Different from the conventional relay selection schemes, the impact of spectrum sensing process as well as the spectrum utilization efficiency of primary users on the performance of DF-based CR relaying networks has been taken into consideration. In particular, the exact closed-form expressions for the figures of merit such as outage probability, BER, and average channel capacity over independent and identically distributed (i.i.d.) Rayleigh fading channels, have been derived in this paper. The validity of the proposed analysis is proven by simulation, which showed that the numerical results are consistent with the theoretical analysis in terms of the outage probability, the BER and the average channel capacity. It is also shown that the full spatial diversity order can always be obtained at the signal-to-noise ratio (SNR) range of [0dB, 15dB] in the presence of multiple potential relays.