In hyperspectral imaging (HSI), stripe noise is one of the most common noise types that adversely affects its application. Convolutional neural networks (CNNs) have contributed to state-of-the-art performance in HSI destriping given their powerful feature extraction and learning capabilities. However, it is difficult to obtain paired training samples for real data. Most CNN destriping methods construct a paired training dataset with simulated stripe noise for network training. However, when the stripe noise of real data is complex, destriping performance of the model is constrained. To solve this problem, this study proposes a real HSI stripe removal method using a toward real HSI stripe removal via direction constraint hierarchical feature cascade network (TRS-DCHC). TRS-DCHC uses the stripe noise extract subnetwork to extract stripe patterns from real stripe-containing HSI data and incorporates clean images to form paired training samples. The destriping subnetwork advantageously utilizes a wavelet transform to explicitly decompose stripe and stripe-free components. It also adopts multi-scale feature dense connections and feature fusion to enrich feature information and deeply mine the discriminate features of stripe and stripe-free components. Our experiments on both simulated and real data of various loads showed that TRS-DCHC features better performance in both simulated and real data compared with state-of-the-art method.