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Deep Neural Networks (DNN) could forget the knowledge about earlier tasks when learning new tasks, and this is known as \textit{catastrophic forgetting}. While recent continual learning methods are capable of alleviating the catastrophic problem on toy-sized datasets, some issues still remain to be tackled when applying them in real-world problems. Recently, the fast mask-based learning method (e.g. piggyback \cite{mallya2018piggyback}) is proposed to address these issues by learning only a binary element-wise mask in a fast manner, while keeping the backbone model fixed. However, the binary mask has limited modeling capacity for new tasks. A more recent work \cite{hung2019compacting} proposes a compress-grow-based method (CPG) to achieve better accuracy for new tasks by partially training backbone model, but with order-higher training cost, which makes it infeasible to be deployed into popular state-of-the-art edge-/mobile-learning. The primary goal of this work is to simultaneously achieve fast and high-accuracy multi task adaption in continual learning setting. Thus motivated, we propose a new training method called \textit{kernel-wise Soft Mask} (KSM), which learns a kernel-wise hybrid binary and real-value soft mask for each task, while using the same backbone model. Such a soft mask can be viewed as a superposition of a binary mask and a properly scaled real-value tensor, which offers a richer representation capability without low-level kernel support to meet the objective of low hardware overhead. We validate KSM on multiple benchmark datasets against recent state-of-the-art methods (e.g. Piggyback, Packnet, CPG, etc.), which shows good improvement in both accuracy and training cost.