Millimeter wave (mmWave) has been regarded as a candidate cellular band for future 5G networks. It exhibits an extension for current cellular bands, where its integrity with massive multiple-input-multiple output (MIMO) and precoding techniques offers a significant capacity improvements. Unfortunately, analog and/or digital precoders are not energy-efficient from mmWave massive MIMO perspectives whereas, one radio frequency (RF) chain per antenna element is required. Accordingly, the hybrid precoding techniques could be introduced as cost-effective solution. It implicates a low dimensional precoding that can be executed in digital domain, followed by a large dimensional analog beam-formers to steer antenna elements. In this paper, we propose a novel low complex and efficient hybrid precoding algorithm to design the analog and digital precoders/combiners for mmWave massive MIMO transceiver. We will show that our proposed precoder approaches the fully digital (unconstrained) precoder with a negligible performance loss that makes it stand as benchmark case. Particularly, we simply design the digital precoding stage based on modified water-filling wherein, the orthogonality criterion among transmitted data streams is guaranteed. Besides, the analog beam-formers are optimally designed via extracting steering angles from an alternative precoder which is derived from a tight and simple upper bound expression. Furthermore, the proposed algorithm will be extended to include the practical analog beam-formers that have limited phase shifter with finite angle resolution. As a result, we will develop a quantization technique, for the analog precoder, with precision up to two bits. Furthermore, we investigate the energy efficiency (EE) performance wherein, EE degradation can be avoided even with one bit of quantization. This will be confirmed through comparing with unconstrained and unquantized precoders. Also, spectral efficiency (SE) performance displays a remarkable gain when it is fairly compared with the state-of-art.