In the development of treatments for cardiovascular diseases, short axis cardiac cine MRI is important for the assessment of various structural and functional properties of the heart. In short axis cardiac cine MRI, Cardiac properties including the ventricle dimensions, stroke volume, and ejection fraction can be extracted based on accurate segmentation of the left ventricle (LV) myocardium. One of the most advanced segmentation methods is based on fully convolutional neural networks (FCN) and can be successfully used to do segmentation in cardiac cine MRI slices. However, the temporal dependency between slices acquired at neighboring time points is not used. Here, based on our previously proposed FCN structure, we proposed a new algorithm to segment LV myocardium in porcine short axis cardiac cine MRI by incorporating convolutional long short-term memory (Conv-LSTM) to leverage the temporal dependency. In this approach, instead of processing each slice independently in a conventional CNN-based approach, the Conv-LSTM architecture captures the dynamics of cardiac motion over time. In a leave-one-out experiment on 8 porcine specimens (3,600 slices), the proposed approach was shown to be promising by achieving average mean Dice similarity coefficient (DSC) of 0.84, Hausdorff distance (HD) of 6.35 mm, and average perpendicular distance (APD) of 1.09 mm when compared with manual segmentations, which improved the performance of our previous FCN-based approach (average mean DSC=0.84, HD=6.78 mm, and APD=1.11 mm). Qualitatively, our model showed robustness against low image quality and complications in the surrounding anatomy due to its ability to capture the dynamics of cardiac motion.