In recent years, learned image compression (LIC) technologies have surpassed conventional methods notably in terms of rate-distortion (RD) performance. Most present learned techniques are VAE-based with an autoregressive entropy model, which obviously promotes the RD performance by utilizing the decoded causal context. However, extant methods are highly dependent on the fixed hand-crafted causal context. The question of how to guide the auto-encoder to generate a more effective causal context benefit for the autoregressive entropy models is worth exploring. In this paper, we make the first attempt in investigating the way to explicitly adjust the causal context with our proposed Causal Context Adjustment loss (CCA-loss). By imposing the CCA-loss, we enable the neural network to spontaneously adjust important information into the early stage of the autoregressive entropy model. Furthermore, as transformer technology develops remarkably, variants of which have been adopted by many state-of-the-art (SOTA) LIC techniques. The existing computing devices have not adapted the calculation of the attention mechanism well, which leads to a burden on computation quantity and inference latency. To overcome it, we establish a convolutional neural network (CNN) image compression model and adopt the unevenly channel-wise grouped strategy for high efficiency. Ultimately, the proposed CNN-based LIC network trained with our Causal Context Adjustment loss attains a great trade-off between inference latency and rate-distortion performance.