The emerging mobile edge computing (MEC) technology has been recently applied to improve adaptive bitrate (ABR) streaming service quality under time-varying wireless channels. In this paper, we consider a heterogeneous multi-user MEC-enabled video streaming network with time-varying wireless channels in sequential time frames. In particular, we aim to design an online joint transcoding and transmission resource allocation algorithm to maximize the ABR streaming user’s quality of experience (QoE) subject to the bandwidth and CPU constraints. The algorithm is “online” in the sense that the bitrate and resource allocation decisions made at each frame depend only on the observation of past events. We formulate the problem as a mixed integer non-linear programming (MINLP) that jointly determines bitrate adaptation, bandwidth allocation, and CPU cycle assignment. To cope with the challenge arising from the coupling decisions of adjacent frames, we propose a low-complexity online algorithm, named OCCA. Specifically, by introducing queueing model constraints, we transform the offline non-conex MINLP problem into a multi-frame problem. Then, we analytically decouple the multi-stage(frame) problem to multiple per-frame convex subproblems that can be solved with high robustness and low computational complexity. We perform simulations with realistic scenarios to evaluate the performance of the proposed algorithm. Results manifest that compared with state-of-the-art approaches, our proposed algorithm can provide 97.84% (on average) extra QoE.