Non-orthogonal multiple access (NOMA) has been a promising technology for 5G communication system. NOMA allows more than one user to utilize the same resource at the same time, which can lead to high performance in terms of spectral efficiency, energy efficiency or fairness. NOMA enables power domain multiplexing and separates the multiplexed signal by using successive interference cancellation (SIC). Therefore, the full benefit of NOMA depends on power allocation. However, in practical system, residual interference caused by SIC process can severely degrade a system performance. In this paper, we propose two power allocation schemes based on deep learning to alleviate the effect of imperfect SIC for downlink NOMA system, including a deep learning-based sum rate power allocation scheme (DL-SRPAS) and a deep learning-based energy-efficient power allocation scheme (DL-EEPAS). our two proposed schemes learn two optimal power allocation schemes provided through exhaustive search. We search the solution of the optimization problems, where two optimization problems are formulated to maximize the sum rate and the energy efficiency subject to a minimum user data rate requirement. The simulation results verify that our two proposed schemes can alleviate the effect of imperfect SIC and outperform two conventional power allocation schemes which maximize the sum rate and the energy efficiency without considering imperfect SIC. In addition, our proposed schemes achieve near-optimal performance with very low computational time.