In this paper, we propose a multiple user-type massive multiple-input-multiple-output (MIMO) system and present power allocation solutions for this proposed network. Unlike conventional massive MIMO systems in which all users are treated equally, the proposed system consists of two types of users: quality-of-service (QoS) users, who are guaranteed to have good and stable quality, and non-QoS users, who are similar to users in conventional massive MIMO systems. We formulate two power allocation optimization problems which guarantee quality-of-service for QoS users and maximize the sum-rate of non-QoS users simultaneously. These two problems are solved by two proposed successive convex approximation algorithms, and we show that these two algorithms surely converge to a local maximum Karush-Kuhn-Tucker point. The numerical results show the effectiveness of our proposed power allocation algorithms in multiple user-type massive MIMO systems.