The flow-dependent left ventricle overload is a well-known complication of the veno-arterial extracorporeal membrane oxygenation in a severe cardiogenic shock, which leads to a distension of the left ventricle and, frequently, to a severe pulmonary edema. Recently, an unloading of the left ventricle using a catheter inserted to the left ventricle and connected to the extracorporeal membrane oxygenation circuit has been proposed. The computational method was used to simulate the blood flow in the extracorporeal membrane oxygenation system with a drainage catheter incorporated to the left ventricle and connected to the inflow part of the extracorporeal membrane oxygenation circuit by a Y-shaped connector. The whole system was modelled in Modelica modelling language. The impact of various catheter sizes (from 5 Fr to 10 Fr) and extracorporeal blood flow values (from 1L/min to 5 L/min) were investigated. In our simulation model, the extracorporeal blood flow only modestly affected the value of volume that was withdrawn from the left ventricle by a catheter. Conversely, the size of the drainage catheter was the principal factor responsible for the achievement of the adequate left ventricle decompression. A 10 Fr drainage catheter, inserted into the left ventricle and connected to the venous part of the ECMO system, presents a promising solution to the unloading of the left ventricle during a extracorporeal membrane oxygenation.