<p>We study the modulational instability of smooth, small-amplitude periodic traveling wave solutions to the generalized Fornberg-Whitham equation. Our approach is based on applying spectral perturbation theory to the associated linearization. We derive a modulational instability index that depends on the nonlinear parameter and the wave number of the underlying wave, and prove that the sufficiently small periodic traveling waves of the generalized Fornberg-Whitham equation are spectrally unstable to long-wavelength perturbations when the modulational instability index is negative, this confirms the well-known Benjamin-Feir instability for the generalized Fornberg-Whitham equation.</p>