Using the linear combination operator method and variational technique improved by Tokuda, we obtain the expression of the effective mass of a strong coupled polaron in an anisotropic quantum dot. Due to the spin–orbit interaction, the effective mass of the polaron splits into two branches. The dependence of effective mass on temperature, electron–phonon coupling strength, transverse and longitudinal confinement lengths, and velocity is discussed by numerical calculation. The theoretical results indicate that the effective mass of the polaron is an increasing function of temperature and electron–phonon coupling strength, but a decreasing function of transverse confinement length, longitudinal confinement length, and velocity. The absolute value of spin splitting effective mass increases with the increase of temperature and spin–orbit coupling parameter, but decreases with the increase of transverse confinement length, longitudinal confinement length, and velocity. Due to the heavy hole characteristic, the spin splitting effective mass is negative.