Non-orthogonal multiple access (NOMA) is a promising spectrally-efficient technology to meet the massive data requirement of the next-generation wireless communication networks. In this paper, we consider a cooperative non-orthogonal multiple access (CNOMA) networks consisting of a base station and two users, where the near user serves as a decode-and-forward relay to help the far user, and investigate the outage probability of the CNOMA users under two different types of channel estimation errors. For both CNOMA users, we derive the closed-form expressions of the outage probability and discuss the asymptotic characteristics for the outage probability in the high signal-to-noise ratio (SNR) regimes. Our results show that for the case of constant variance of the channel estimation error, the outage probability of two users are limited by a performance bottleneck which related to the value of the error variance. In contrast, there is no such performance bottleneck for the outage probability when the variance of the channel estimation error deceases with SNR, and in this case the diversity gain is fully achieved by the far user.