In order to address the problem of spectrum sensing with random presence and absence of primary user's signal in cognitive radios, a novel energy based spectrum sensing method is proposed. The method first assumes that the departuring process and the arriving process of the primary user's signal are possion random processes. When a cognitive user tries to access a spectrum, the energy of the collected samples is combined linearly according to the departure rate of Possion random process and then the corresponding threshold is calculated to decide whether there is a primary user or not. If the primary user is absent, the cognitive user accesses and the spectrum is used. When the cognitive user is using the spectrum, it also combines the energy of the collected samples linearly according to the arrival rate of Possion random process and calculates the corresponding threshold to test whether the primary user is arriving or not. If the primary user is arriving, the cognitive user vacates this spectrum immediately. Simulation results show that compared with traditional energy based detection method, the proposed method can work efficiently with random presence and absence of primary user's signal.