The left ventricle function is to pump the oxygenated blood through the circulatory system. Ejection fraction is the main noninvasive parameter for detecting heart disease (healthy >55%), and it is thought to be the main parameter affecting efficiency. However, the effects of other parameters on efficiency have yet to be investigated. We investigate the effect of heart rate and left ventricle shape by carrying out 3D numerical simulations of a left ventricle at different heart rates and perturbed geometries under constant, normal ejection fraction. The simulation using the immersed boundary method provide the 3D flow and pressure fields, which enable direct calculation of a new hemodynamic efficiency (H-efficiency) parameter, which does not depend on any reference pressure. The H-efficiency is defined as the ratio of flux of kinetic energy (useful power) to the total cardiac power into the left ventricle control volume. Our simulations show that H-efficiency is not that sensitive to heart rate but is maximized at around normal heart rate (72 bpm). Nevertheless, it is more sensitive to the shape of the left ventricle, which affects the H-efficiency by as much as 15% under constant ejection fraction.