In recent years, the application of the CRISPR/Cas system has enabled gene editing technology to flourish. However, the low-specificity of some guide RNAs (gRNAs) may lead to off-target effects limiting the wider applicability of the technology in medicine. Most of the existing neural network-based machine learning models are only capable of providing point estimates of (off-)target activity for a given gRNA – (off-)target DNA pair, and have a limited ability to capture uncertainty. We propose CRISPR-DBA, a Bayesian-based neural network framework to address this challenge. Instead of introducing new parameters to simulate model uncertainty, the proposed method is the first neural network-based machine learning model that utilizes dropout layer information to extract distribution of off-target cleavage activities for CRISPR/Cas gRNAs. Our method conducts evaluation across various datasets from different studies, showing that proposed CRISPR-DBA compares favourably with machine learning models equipped with traditional uncertainty estimation approaches such as Gaussian Processes. It also outperforms an existing probabilistic model in confidence performance. The three key features of the proposed method include 1) the ability to generate trustworthy predictions by providing extra confidence readings of prediction; 2) reduction of complexity compared to approaches equipped with similar functionality; 3) adaptability in terms of being able to utilise existing model architectures developed in the field. The datasets and source code supporting this study can be found at https://github.com/xccao/crisprDBA.