Background Polypharmacy is a type of treatment that involves the concurrent use of multiple medications. Drugs may interact when they are used simultaneously. So, understanding and mitigating polypharmacy side effects are critical for patient safety and health. Since the known polypharmacy side effects are rare and they are not detected in clinical trials, computational methods are developed to model polypharmacy side effects. Results We propose a neural network-based method for polypharmacy side effects prediction (NNPS) by using novel feature vectors based on mono side effects, and drug–protein interaction information. The proposed method is fast and efficient which allows the investigation of large numbers of polypharmacy side effects. Our novelty is defining new feature vectors for drugs and combining them with a neural network architecture to apply for the context of polypharmacy side effects prediction. We compare NNPS on a benchmark dataset to predict 964 polypharmacy side effects against 5 well-established methods and show that NNPS achieves better results than the results of all 5 methods in terms of accuracy, complexity, and running time speed. NNPS outperforms about 9.2% in Area Under the Receiver-Operating Characteristic, 12.8% in Area Under the Precision–Recall Curve, 8.6% in F-score, 10.3% in Accuracy, and 18.7% in Matthews Correlation Coefficient with 5-fold cross-validation against the best algorithm among other well-established methods (Decagon method). Also, the running time of the Decagon method which is 15 days for one fold of cross-validation is reduced to 8 h by the NNPS method. Conclusions The performance of NNPS is benchmarked against 5 well-known methods, Decagon, Concatenated drug features, Deep Walk, DEDICOM, and RESCAL, for 964 polypharmacy side effects. We adopt the 5-fold cross-validation for 50 iterations and use the average of the results to assess the performance of the NNPS method. The evaluation of the NNPS against five well-known methods, in terms of accuracy, complexity, and running time speed shows the performance of the presented method for an essential and challenging problem in pharmacology. Datasets and code for NNPS algorithm are freely accessible at https://github.com/raziyehmasumshah/NNPS.