The enhancement of plasma heating efficiency is important for realizing inertial fusion energy, which follows the ignition achieved with the laser-indirect-drive central-ignition approach. An increase in the relativistic electron beam (REB) generation efficiency, an improvement in REB directivity, and the optimization of REB energy distribution are key for enhancing the heating efficiency in the fast ignition approach using laser-produced REBs. Here, we show that an extreme ultra-high contrast of the heating laser pulse is essential for efficiently heating high-density plasma using the fast-ignition approach of inertial confinement fusion. A heating efficiency enhancement of more than 2 x was obtained with a high-contrast heating laser compared to that obtained with the lower-contrast LFEX laser. The enhanced heating efficiency is ascribed to the significant reduction of the REB divergence and the increased number of electrons injected into the plasma. The interaction between the high-contrast laser and a plasma suppresses excessive acceleration of the REB The high contrast shortens the distance between the REB generation point and the high-density plasma. However, it is clarified that ultra-high contrast reduces the laser absorption fraction, future research on improving laser absorption for high-contrast lasers is required.