Adaptive compressed spectrum sensing (ACSS) can effectively save sampling resources in wideband spectrum sensing. Almost all of the existing ACSS algorithms are based on the discrete multitone signal model. However, real-world spectra are always multiband signals. In this paper, we derive mathematical models and algorithms enabling the ACSS suitable for multiband signals, which can save sampling resources and has lower computational complexity. Firstly, we introduce the multicoset sampling system into ACSS to sample multiband signals. Besides, we propose a leave-one-out cross-validation (LOOCV) based ACSS scheme with low sampling costs. To save sampling resources, we choose only one sampling channel as a testing subset to validate reconstructed signal and repeat this several times with different sampling channels. Then, we use the mean of the multiple validation results to determine the accuracy of the reconstructed signal. To reduce computational complexity, we propose a LOOCV-ACSS algorithm, in which we only perform the least square method several times in the LOOCV procedure, rather than the complicated compressed sensing reconstruction algorithms. Numerical simulations and real-world signal test results demonstrate that our derivation and algorithms are effective to reduce the sampling cost while keeping the same performance as conventional algorithms.