<p>For solving the complex conjugate and transpose Sylvester matrix equations, many gradient based iterative (GI)-like algorithms have been proposed, which are a kind of efficient methods for matrix equations. In this paper, we apply the momentum acceleration technique to the relaxed GI (RGI) (J. Appl. Math. Comput., 67 (2021) 317-341), modified RGI (MRGI) and accelerated RGI (ARGI) algorithms (Numer. Algorithms, 97 (2024) 1955-2009) to improve their convergence speeds. By introducing the momentum factors and terms containing the computed results of two previous iterations into the ARGI, MRGI and RGI algorithms, we design the momentum acceleration-based ARGI (MAARGI), momentum acceleration-based MRGI (MAMRGI) and momentum acceleration-based RGI (MARGI) algorithms, respectively. We investigate the convergence properties of the three proposed iterative algorithms. Also, we deduce the optimal momentum factor and convergence factor of the MARGI algorithm, and quasi-optimal momentum factor for MAARGI algorithm, which are vital to their implementations. Lastly, numerical examples including the applications in time-varying linear system and image processing are performed to demonstrate the validities, robustness and advantages of the proposed algorithms. And numerical examples also illustrate that the optimal and quasi-optimal momentum factors for the MARGI and MAARGI algorithms are feasible and efficient.</p>