Spectrum sharing between primary and secondary systems is discussed in this paper. A two-phase spectrum sharing protocol is proposed by using analog network coding (ANC), in which a secondary (cognitive) user acts as a relay to assist the bidirectional primary transmissions. ANC is employed for two-way relaying between the two primary users, and spectrum sharing is achieved by superimposing the secondary signal on the network-coded primary signals at the secondary relay. We analytically derive the outage probability and the ergodic capacity for the primary users under our proposed two-phase protocol and characterize the spectrum sharing regions within which the two-phase spectrum sharing protocol can achieve higher (or at least equal) outage performance for the primary system than direct transmission without spectrum sharing. The lower and upper bounds of the outage probability and the ergodic capacity for the secondary user are developed as well. Results show that, if an appropriate power split is adopted at the secondary relay, our proposed spectrum sharing protocol can achieve even better performance for the primary system than direct transmission without spectrum sharing while, at the same time, providing spectrum opportunities for the secondary transmission. Furthermore, because much more power can be allowed in our protocol to transmit the secondary messages, it can offer more benefits to the secondary system than another three-phase spectrum sharing protocol based on decode-and-forward (DF) network coding.