<p>Given the importance of fractional delay differential equations in various applications, this work focuses on introducing an effective scheme for solving these equations. The first step of the proposed scheme involves converting the desired equation into a Volterra integral equation. The Galerkin wavelet method is then employed to transform the Volterra integral equation into a system of algebraic equations. In its linear form, an appropriate threshold parameter can be used to reduce the elements of the coefficient matrix, resulting in decreased computational costs. Convergence and stability analyses are conducted, and several numerical experiments illustrate the method’s efficiency, flexibility, and accuracy. The main result is that the proposed method can effectively solve both linear and nonlinear fractional delay differential equations with a high level of accuracy while reducing computational costs, thanks to the properties of multiwavelets.</p>