Abstract: In cognitive radio, secondary users detect primary user’s signal in a specific spectrum band to determine whether the band can be reused. For primary user detection, both of the detection accuracy and detection time are key performance indexes. This paper analyzed the detection time of decision fusion based primary user detection subject to the constraints of required detection accuracy. Two examples of AND rule as well as OR rule based primary user detection were considered, and analytic expressions for their average time were deduced. Moreover, by comparing the average detection time, this paper proved that OR rule was superior to AND rule from detection time point of view under the same accuracy constraints. Numerical simulation verified all the conclusions in this paper, and demonstrated that superiority of OR rule in detection time over AND rule was greater in the scenarios with higher accuracy constraints or lower signal to noise ratios.