The automatic diagnosis of cardiovascular diseases has received much attention in the deep learning field. In this context, the segmentation of the left ventricle endocardium constitutes a major task in diagnosing heart conditions such as health failure and hypertrophic cardiomyopathy. The objective of this paper is to propose a "deep convolution network" for segmenting the internal cavity of the left ventricle (endocardium) using MRI images. In particular, we design an improved UNET model which handles additional inception modules for efficiently segmenting the internal cavity of the left ventricle. Our approach has been validated on the Sunnybrook Cardiac Data (SCD) dataset and has showed promising results in terms of precision. More specifically, the improved UNET largely outperforms the baseline UNET model and many existing state-of-the-art methods.