Machine learning and computer vision algorithms can provide a precise and automated interpretation of medical videos. The segmentation of the left ventricle of echocardiography videos plays an essential role in cardiology for carrying out clinical cardiac diagnosis and monitoring the patient’s condition. Most of the developed deep learning algorithms for video segmentation require an enormous amount of labeled data to generate accurate results. Thus, there is a need to develop new semi-supervised segmentation methods due to the scarcity and costly labeled data. In recent research, semi-supervised learning approaches based on graph signal processing emerged in computer vision due to their ability to avail the geometrical structure of data. Video object segmentation can be considered as a node classification problem. In this paper, we propose a new approach called GraphECV based on the use of graph signal processing for semi-supervised learning of video object segmentation applied for the segmentation of the left ventricle in echordiography videos. GraphECV includes instance segmentation, extraction of temporal, texture and statistical features to represent the nodes, construction of a graph using K-nearest neighbors, graph sampling to embed the graph with small amount of labeled nodes or graph signals, and finally a semi-supervised learning approach based on the minimization of the Sobolov norm of graph signals. The new algorithm is evaluated using two publicly available echocardiography videos, EchoNet-Dynamic and CAMUS datasets. The proposed approach outperforms other state-of-the-art methods under challenging background conditions.