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While RRAM crossbar-based In-Memory Computing (IMC) has proven highly effective in accelerating Deep Neural Networks (DNNs) inference, RRAM-based on-device training is less explored due to its high energy consumption of weight re-programming and cells' low endurance problem. Besides, emerging trends indicate a need for on-device continual learning which sequentially acquires knowledge from multiple tasks to enhance user's experiences and eliminate data privacy concerns. However, learning on each new task leads to forgetting prior learned knowledge on prior tasks, which is known as catastrophic forgetting. To address these challenges, we are the first to propose a novel training framework, Hyb-Learn, for enabling on-device continual learning with a hybrid RRAM/SRAM IMC architecture design. Specifically, when training each new arriving task, our approach first partitions the model into two groups based on the proposed task-correlated PE-wise correlation to freeze or re-training, and correspondingly mapping to RRAM and SRAM, respectively. In practice, the RRAM stores frozen weights with strong task correlation to prior tasks to eliminate the high cost of weight reprogramming issue of RRAM, while the SRAM stores the remaining weights that will be updated. Furthermore, to maximize the freezing ratio for improving training efficiency while maintaining accuracy and mitigating catastrophic forgetting, we incorporate self-supervised learning algorithms that are initialized from a pre-trained model for training each new task.