Federated learning (FL) over wireless networks offers a promising approach to enable decentralized machine learning among massive mobile edge nodes while ensuring privacy in training data. However, the convergence speed of FL is limited by the straggler effect, which arises from heterogeneous nodes, wireless fading channels, and non-independently and identically distributed (non-IID) training data. In this paper, we consider an adaptive semi-asynchronous FL to mitigate the straggler effect, by dynamically selecting subsets of nodes over time to synchronize the global model. We jointly optimize the node scheduling and computing/communication resource allocation to minimize the completion time required for convergence of the adaptive semi-asynchronous FL. Leveraging the convergence condition of semi-asynchronous FL, we further propose a greedy heuristic policy for node scheduling while tackling the remaining computing/communication resource allocation problem by exploiting a hidden convexity. Simulation results on open datasets demonstrate that, compared with existing FL algorithms, our proposed adaptive semi-asynchronous algorithm can significantly lower the latency of FL convergence.