Objective. The classification of olfactory-induced electroencephalogram (olfactory EEG) signals has potential applications in disease diagnosis, emotion regulation, multimedia, and so on. To achieve high-precision classification, numerous EEG channels are usually used, but this also brings problems such as information redundancy, overfitting and high computational load. Consequently, channel selection is necessary to find and use the most effective channels. Approach. In this study, we proposed a multi-strategy fusion binary harmony search (MFBHS) algorithm and combined it with the Riemannian geometry (RG) classification framework to select the optimal channel sets for olfactory EEG signal classification. MFBHS was designed by simultaneously integrating three strategies into the binary harmony search (BHS) algorithm, including an opposition-based learning strategy (OBL) for generating high-quality initial population, an adaptive parameter strategy (APS) for improving search capability, and a bitwise operation strategy (BOS) for maintaining population diversity. It performed channel selection directly on the covariance matrix of EEG signals, and used the number of selected channels and the classification accuracy computed by a Riemannian classifier to evaluate the newly generated subset of channels. Main results. With five different classification protocols designed based on two public olfactory EEG datasets, the performance of MFBHS was evaluated and compared with some state-of-the-art algorithms. Experimental results reveal that our method can minimize the number of channels while achieving high classification accuracy compatible with using all the channels. In addition, cross-subject generalization tests of MFBHS channel selection show that subject-independent channels obtained through training can be directly used on untrained subjects without greatly compromising classification accuracy. Significance. The proposed MFBHS algorithm is a practical technique for effective use of EEG channels in olfactory recognition.