This article investigates fairness-aware transmission in a wireless powered communication network (WPCN), in which a group of adjacent users receive radio frequency energy and then cooperatively transmit information to a remote access point (AP) by using the harvested energy with time division multiple access (TDMA) scheme. Considering the constraints of practical energy harvesting electric circuits, a non-linear energy harvesting model is adopted in this paper. To guarantee both throughput fairness and signal-to-noise-ratio (SNR) fairness among users in the group, we propose a cooperative transmission protocol which contains three phases: wireless energy transmission (WET) phase, single information transmission phase and cooperative information transmission phase. Each user harvests wireless energy in WET phase, and then divides the harvested energy into two parts to be used in the rest two phases. In single information transmission phase, each user broadcasts its information to the AP and all the other users. In cooperative information transmission phase, all the users transmit information jointly to the AP. At the AP, the same signals in cooperative information transmission phase are combined with these in single information transmission phase by using maximum ratio combining (MRC) method. The common SNR of the received signals at the AP from all the users is achieved in both single information transmission phase and cooperative information transmission phase. Furthermore, the throughput fairness is achieved by common SNR and equal time allocation for information transmission at each user. Besides, we optimize the max-min throughput by joint WET time and harvested energy allocation. The optimal time allocation ratio and harvested energy allocation ratio are derived in closed forms. The cooperative diversity gain is achieved and numerical results demonstrate that the proposed protocol has low complexity and high reliability. Moreover, it also achieves a higher minimum throughput and is more energy-efficient in harsh transmission condition than other transmission protocols in the literature.