The Beijing-Arizona Sky Survey (BASS) Data Release 3 (DR3) catalogue was released in 2019, which contains the data from all BASS and the Mosaic z-band Legacy Survey (MzLS) observations during 2015 January and 2019 March, about 200 million sources. We cross-match BASS DR3 with spectral databases from the Sloan Digital Sky Survey (SDSS) and the Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST) to obtain the spectroscopic classes of known samples. Then, the samples are cross-matched with ALLWISE database. Based on optical and infrared information of the samples, we use the XGBoost algorithm to construct different classifiers, including binary classification and multiclass classification. The accuracy of these classifiers with the best input pattern is larger than 90.0 per cent. Finally, all selected sources in the BASS DR3 catalogue are classified by these classifiers. The classification label and probabilities for individual sources are assigned by different classifiers. When the predicted results by binary classification are the same as multiclass classification with optical and infrared information, the number of star, galaxy and quasar candidates is separately 12 375 838 (P_S>0.95), 18 606 073 (P_G>0.95) and 798 928 (P_Q>0.95). For these sources without infrared information, the predicted results can be as a reference. Those candidates may be taken as input catalogue of LAMOST, DESI or other projects for follow up observation. The classified result will be of great help and reference for future research of the BASS DR3 sources.