The ergodic capacity was studied that of relay selection cooperative communication network systems. The closed-form expressions of some important factors, including, the probability density function, the cumulative distribution function, and the ergodic capacity, were derived by considering the opportunistic selection and the partial selection of decode-and-forward relays, respectively, with independent and identically distributed rayleigh fading wireless links assumed. The results show the diversity degree can be effectively improved by relay selection techniques. Besides, the ergodic capacity can be substantially influenced by the number of relays, and the signal-to-noise ratio (SNR). The closed-form expressions are verified by numerical simulation. The experiment results show that the non-outage channel capacity can reach to ergodic capacity though optimal data transmission rate being adjusted by the feedback channel state information.