Dynamic spectrum access has become a focal issue recently, in which identifying the available spectrum plays a rather important role. Lots of work has been done concerning secondary user (SU) synchronously accessing primary user's (PU's) network. However, on one hand, SU may have no idea about PU's communication protocols; on the other, it is possible that communications among PU are not based on synchronous scheme at all. In order to address such problems, this paper advances a strategy for SU to search available spectrums with asynchronous MAC-layer sensing. With this method, SUs need not know the communication mechanisms in PU's network when dynamically accessing. We will focus on four aspects: 1) strategy for searching available channels; 2) vacating strategy when PUs come back; 3) estimation of channel parameters; 4) impact of SUs' interference on PU's data rate. The simulations show that our search strategy not only can achieve nearly 50% less interference probability than equal allocation of total search time, but also well adapts to time-varying channels. Moreover, access by our strategies can attain 150% more access time than random access. The moment matching estimator shows good performance in estimating and tracing time-varying channels.