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Recent works on learned image compression perform encoding and decoding processes in a full-resolution manner, resulting in two problems when deployed for practical applications. First, parallel acceleration of the autoregressive entropy model cannot be achieved due to serial decoding. Second, full-resolution inference often causes the out-of-memory(OOM) problem with limited GPU resources, especially for high-resolution images. Block partition is a good design choice to handle the above issues, but it brings about new challenges in reducing the redundancy between blocks and eliminating block effects. To tackle the above challenges, this paper provides a learned block-based hybrid image compression (LBHIC) framework. Specifically, we introduce explicit intra prediction into a learned image compression framework to utilize the relation among adjacent blocks. Superior to context modeling by linear weighting of neighbor pixels in traditional codecs, we propose a contextual prediction module (CPM) to better capture long-range correlations by utilizing the strip pooling to extract the most relevant information in neighboring latent space, thus achieving effective information prediction. Moreover, to alleviate blocking artifacts, we further propose a boundary-aware postprocessing module (BPM) with the edge importance taken into account. Extensive experiments demonstrate that the proposed LBHIC codec outperforms the VVC, with a bit-rate conservation of 4.1%, and reduces the decoding time by approximately 86.7% compared with that of state-of-the-art learned image compression methods.