Although underlay spectrum sharing has been shown as a promising technique to promote the spectrum utilization in cognitive radio networks (CRNs), it may suffer bad secondary performance due to the strict power constraints imposed at secondary systems and the interference from primary systems. In this paper, we propose a two-phase based cooperative transmission protocol with the interference cancellation (IC) and best-relay selection to improve the secondary performance in underlay models under stringent power constraints while ensuring the primary quality-of-service (QoS). In the proposed protocol, IC is employed at both the secondary relays and the secondary destination, where the IC-based best-relay selection and cooperative relaying schemes are well developed to reduce the interference from primary systems. The closed-form expression of secondary outage probability is derived for the proposed protocol over Rayleigh fading channels. Simulation results show that, with a guaranteed primary outage probability, the proposed protocol can achieve not only lower secondary outage probability but also higher secondary diversity order than the traditional underlay case.