Single frame infrared small target (SIRST) detection is useful for many practical applications, such as maritime rescue. However, SIRST detection is challenging due to the low-contrast between small targets and noisy background in infrared images. To address this challenge, we propose a novel FC3-Net by exploring feature compensation and cross-level correlation for SIRST detection. Specifically, FC3-Net consists of a Fine-detail guided Multi-level Feature Compensation (F-MFC) module, and a Cross-level Feature Correlation (CFC) module. The F-MFC module aims to compensate the information loss of details caused by the downsampling layers in convolutional neural networks (CNN) via aggregating features from multiple adjacent levels, so that the detail features of small targets can be propagated to the deeper layers of the network. Besides, to suppress the side impact of background noise, the CFC module constructs an energy filtering kernel based on the higher-level features with less background noise to filter out the noise in the middle-level features, and fuse them with the low-level ones to learn a strong target representation. Putting them together into the encoder-decoder structure, our FC3-Net could produce an accurate target mask with fine shape and details. Experiment results on the public NUAA-SIRST and IRSTD-1k datasets demonstrate that the proposed FC3-Net outperforms state-of-the-art methods in terms of both pixel-level and object-level metrics. The code will be released at https://github.com/IPIC-Lab/SIRST-Detection-FC3-Net.