Unmanned aerial vehicles (UAVs) have gained much popularity for a wide variety of applications which do not require human operator, but also face the spectrum scarcity problem. In order to address this problem, a cognitive UAV network (CUAVN) framework based on cognitive radio (CR) technology is formulated in this paper. On the basis of this, sequential probability ratio test (SPRT) is used as a fundamental cooperative spectrum sensing (CSS) scheme to significantly reduce the average number sample, but the uncertainty of its detection delay has the negative impact on the spectrum sensing performance of CUAVNs. Considering the location flexibility and uneven distribution density of UAVs, we design an intra-frame CSS structure, with aim of achieving CSS between micro-sensing slots. Furthermore, a sequential maximal truncation (SMT) is proposed to realize a quick spectrum sensing for delay-constraint CUAVNs. Compared to uniform tail truncation (UTT), simulation results show that the proposed quick multi-band spectrum sensing with the help of SMT requires fewer sensing times in support of better sensing performance, especially under a strict delay constraint.