Cuff-less and continuous blood pressure (BP) measurement has recently become an active research area in the field of remote healthcare monitoring. There is a growing demand for automated BP estimation and monitoring for various long-term and chronic conditions. Automated BP monitoring can produce a good amount of rich health data, which increases the chance of early diagnosis and treatments that are critical for a long-term condition such as hypertension and Cardiovascular diseases (CVDs). However, mining and processing this vast amount of data is challenging, which is aimed to address in this research. We employed a continuous wavelet transform (CWT) and a deep convolutional neural network (CNN) to estimate the BP. The electrocardiogram (ECG), photoplethysmography (PPG) and arterial blood pressure (ABP) signals were extracted from the online Medical Information Mart for Intensive Care (MIMIC III) database. The scalogram of each signal was created and used for training and testing our proposed CNN model that can implicitly learn to extract the descriptive features from the training data. This study achieved a promising BP estimation approach has been achieved without employing engineered feature extraction that is comparable with previous works. Experimental results demonstrated a low root mean squere error (RMSE) rate of 3.36 mmHg and a high accuracy of 86.3% for BP estimations. The proposed CNN-based model can be considered as a reliable and feasible approach to estimate BP for continuous remote healthcare monitoring.