The reliable state of health (SOH) estimation of lithium-ion batteries ensures the safety and efficiency of electric vehicles and energy storage systems. However, when the battery is under varied and incomplete working conditions, the estimation of SOH is still challenging due to the diversity and irregularity of the health indicators. Thus, an algorithm with strongly nonlinear capability is required. In this paper, a dilated residual regression network is presented for estimating the SOH of lithium-ion batteries under varied and incomplete charging conditions. The incremental capacity and voltage are extracted as feature pairs from varied conditions with fixed charging ranges to build the feature matrix. Then the dilated convolution initially extracts the shallow features of the feature matrix, which is subsequently fed into the deep residual network to estimate the SOH of the batteries. The accuracy and robustness of the proposed method are verified by comparison with machine learning algorithms and shallow convolutional networks. The interpretability of the proposed deep model is further improved by analyzing the occlusion sensitivity map of shallow and deep layers. These efforts enhance the application of SOH estimation methods in the real world.