The balanced steady-state free precession (bSSFP) MR sequence is frequently used in clinics, but is sensitive to off-resonance effects, which can cause banding artifacts. Often multiple bSSFP datasets are acquired at different phase cycling (PC) angles and then combined in a special way for banding artifact suppression. Many strategies of combining the datasets have been suggested for banding artifact suppression, but there are still limitations in their performance, especially when the number of phase-cycled bSSFP datasets is small. The purpose of this study is to develop a learning-based model to combine the multiple phase-cycled bSSFP datasets for better banding artifact suppression. Multilayer perceptron (MLP) is a feedforward artificial neural network consisting of three layers of input, hidden, and output layers. MLP models were trained by input bSSFP datasets acquired from human brain and knee at 3T, which were separately performed for two and four PC angles. Banding-free bSSFP images were generated by maximum-intensity projection (MIP) of 8 or 12 phase-cycled datasets and were used as targets for training the output layer. The trained MLP models were applied to another brain and knee datasets acquired with different scan parameters and also to multiple phase-cycled bSSFP functional MRI datasets acquired on rat brain at 9.4T, in comparison with the conventional MIP method. Simulations were also performed to validate the MLP approach. Both the simulations and human experiments demonstrated that MLP suppressed banding artifacts significantly, superior to MIP in both banding artifact suppression and SNR efficiency. MLP demonstrated superior performance over MIP for the 9.4T fMRI data as well, which was not used for training the models, while visually preserving the fMRI maps very well. Artificial neural network is a promising technique for combining multiple phase-cycled bSSFP datasets for banding artifact suppression.