State-of-the-art neural implicit surface representations have achieved impressive results in indoor scene reconstruction by incorporating monocular geometric priors as additional supervision. However, we have observed that multi-view inconsistency between such priors poses a challenge for high-quality reconstructions. In response, we present NC-SDF, a neural signed distance field (SDF) 3D reconstruction framework with view-dependent normal compensation (NC). Specifically, we integrate view-dependent biases in monocular normal priors into the neural implicit representation of the scene. By adaptively learning and correcting the biases, our NC-SDF effectively mitigates the adverse impact of inconsistent supervision, enhancing both the global consistency and local details in the reconstructions. To further refine the details, we introduce an informative pixel sampling strategy to pay more attention to intricate geometry with higher information content. Additionally, we design a hybrid geometry modeling approach to improve the neural implicit representation. Experiments on synthetic and real-world datasets demonstrate that NC-SDF outperforms existing approaches in terms of reconstruction quality.