Artificial intelligence (AI) is widely adopted in various services and has become the key technology to promote industrial upgrading. However, AI service infrastructures in 5G are independent relative to the network and are difficult to be controlled collaboratively in real-time. Fortunately, native AI wireless networks can orchestrate and schedule the communication, computation, data, and AI model resources to efficiently deliver diverse and high-performance AI services. Therefore, this paper considers a task scheduling and resource allocation scheme for AI training services in native AI wireless networks, allowing for flexible computing server selection, data quality adjustment, and resource allocation. To provide results without additional subjective preference information, we establish a multiple objective integer programming problem to increase the accuracy of trained AI models while reducing the task delay. Then, an NSG-TSRA heuristic algorithm is proposed to obtain the approximate solution of the Pareto-optimal set. Finally, we conduct simulations to verify the feasibility and performance of the proposed scheme.