Effective capacity (EC) is an important performance metric for a time-varying wireless channel in order to evaluate the communication rate in the physical layer (PHL) while satisfying the statistical delay quality of service (QoS) requirement in data-link layer (DLL). This paper analyzes EC of amplify-and-forward wireless relay network with different relay selection (RS) protocols. First, through the analysis of the probability density function (PDF) of received signal-to-noise ratio (SNR), the exact expressions of EC for direct transmission (DT), random relay (RR), random relay with direct transmission (RR-WDT), best relay (BR) protocols are derived. Then a novel best relay with direct transmission (BR-WDT) protocol is proposed to maximize EC and an exact expression of EC for BR-WDT protocol is developed. Simulations demonstrate that the derived analytical results well match those of Monte-Carlo simulations. The proposed BR-WDT protocol can always achieve larger EC than other protocols while guaranteeing the delay QoS requirement. Moreover, the influence of distance between source and relay on EC is discussed, and optimal relay position for different RS protocols is estimated. Furthermore, EC of all protocols becomes smaller while delay QoS exponent becomes larger, and EC of BR-WDT becomes better while the number of relays becomes larger.