In the original BB84 quantum key distribution protocol, the states are prepared and measured randomly, which lose the unmatched detection results. To improve the sifting efficiency, biased bases selection BB84 protocol is proposed. Meanwhile, a practical quantum key distribution protocol can only transmit a finite number of signals, resulting in keys of finite length. The previous techniques for finite-key analysis focus mainly on the statistical fluctuations of the error rates and yields of the qubits. However, the prior choice probabilities of the two bases also have fluctuations by taking into account the finite-size effect. In this paper, we discuss the security of biased decoy state BB84 protocol with finite resources by considering all of the statistical fluctuations. The results can be directly used in the experimental realizations.