A numerical method is proposed for solving fractional pantograph differential equations with boundary conditions. First, the problem is transformed into an equivalent integral equation. Then, the unknown function is approximated using the generalized Jacobi wavelet basis functions. Gauss-Jacobi quadrature formula together with a suitable set of collocation points help us to reduce the main problem into a system of nonlinear algebraic equations. Finally, an illustrative example and its results are given.