Compressed video super-resolution (SR) aims to generate high-resolution (HR) videos from the corresponding low-resolution (LR) compressed videos. Recently, some compressed video SR methods attempt to exploit the spatio-temporal information in the frequency domain, showing great promise in super-resolution performance. However, these methods do not differentiate various frequency subbands spatially or capture the temporal frequency dynamics, potentially leading to suboptimal results. In this paper, we propose a deep frequency-based compressed video SR model (FCVSR) consisting of a motion-guided adaptive alignment (MGAA) network and a multi-frequency feature refinement (MFFR) module. Additionally, a frequency-aware contrastive loss is proposed for training FCVSR, in order to reconstruct finer spatial details. The proposed model has been evaluated on three public compressed video super-resolution datasets, with results demonstrating its effectiveness when compared to existing works in terms of super-resolution performance (up to a 0.14dB gain in PSNR over the second-best model) and complexity.