In this paper, we investigate the uplink transmission in a cellular network from a UAV and ground users to ground base stations (BSs). Specifically, we aim to maximize the sum rate of the uplink from the UAV to ground BSs in a specific idle frequency band as well as from the co-channel users to their associated BSs by optimizing precoding vectors at UAV. To mitigate the interference, we apply successive interference cancellation (SIC) not only to the BSs connected with UAV using non-orthogonal multiple access (NOMA) for transmission, but also to other BSs communicating with ground users in the same band. The precoding optimization problem with constraints on the SIC decoding and the uplink transmission rate is formulated, which is non-convex and intractable. Thus, we introduce auxiliary variables and apply first-order approximations based on Taylor expansion to convert it into a second-order cone programming. An iterative algorithm is proposed with low complexity to calculate the solution to the non-convex precoding optimization problem. Numerical results demonstrate the effectiveness of our proposed scheme.