Non-orthogonal multiple access (NOMA) has received tremendous attention for the development of 5G and beyond wireless networks. Power-domain NOMA works on the concept of assigning varying power levels to users within the same frequency and time block. In this paper we propose a novel power allocation approach that uses the Zipf distribution law that satisfies the basic condition of a NOMA system. The Zipf PA is characterized by the simplicity and ease of implementation that allows to extend the capacity of the system to support a large number of users. The numerical results show that the system achieves high throughput and energy efficiency without any parameter optimization constraints as well as improved capacity by increasing the number of users compared to the NOMA system with existing power allocation techniques.