In this work, we aim to learn a unified vision-based policy for a multi-fingered robot hand to manipulate different objects in diverse poses. Though prior work has demonstrated that human videos can benefit policy learning, performance improvement has been limited by physically implausible trajectories extracted from videos. Moreover, reliance on privileged object information such as ground-truth object states further limits the applicability in realistic scenarios. To address these limitations, we propose a new framework ViViDex to improve vision-based policy learning from human videos. It first uses reinforcement learning with trajectory guided rewards to train state-based policies for each video, obtaining both visually natural and physically plausible trajectories from the video. We then rollout successful episodes from state-based policies and train a unified visual policy without using any privileged information. A coordinate transformation method is proposed to significantly boost the performance. We evaluate our method on three dexterous manipulation tasks and demonstrate a large improvement over state-of-the-art algorithms.