Heart disease is one of the leading causes of death globally, which takes 17.9 million lives each year. The existing heart disease prediction techniques have a gap that does not consider the smoking attributes from the heart disease data. So, the accuracy is based on the limited number of medical data and the deep learning model. The existing deep learning models which use the Recurrent Neural Network (RNN) for heart disease prediction consume more processing and analysing time, mainly due to the delay of data retrieval. This delay causes the prediction process to become slower and leads to a moderate prediction only. The backpropagation of the RNN with an update gate and internal memory to carry the updated data cause a minor data glitch that leads to lower accuracy. Therefore, an efficient heart disease prediction model is very crucial to provide early detection among patients. This research proposes a Heart Disease Risk Prediction Model (HDRPM) with an enhanced RNN to improve the prediction accuracy using Framingham heart disease datasets. The specificity and sensitivity are imposed to improve the quality of the predictions. Sensitivity measure is used for detecting patients with heart disease perfectly and specificity measure is used for detecting patients without the disease perfectly. Besides the accuracy and quality of the prediction problem, the imbalance of minority classes in the dataset occurred in most deep learning prediction fields. This research aims to improve the quality of imbalanced Framingham datasets using Synthetic Minority Over-sampling Technique (SMOTe), which will synthetic instances in a small class to be equalized. The existing RNN model faces vanishing gradients that impede the learning of long data sequences. These gradients that carry information in the RNN cells will become smaller gradually till it minimises the parameter updates and leads to poor learning. For this purpose, the presence of multiple Gated Recurrent Unit (GRU) is used to overcome the vanishing gradients and ensure the hidden layers. The neurons of RNN rapidly cater for the essential information during the training and validation phase of the HDRPM. The integration of multiple GRU with the RNN, operating on the Tensorflow as back-end and Keras as the core for the neural network library has increased the performance of the proposed model. The proposed model provides up to 98.78%, the highest accuracy achieved compared to related previous work, which is a quantum neural network model with 98.57. This HDRPM is expected to significantly contribute to early detection of heart disease patients.