We investigate the wave-breaking mechanism of solutions to a Fornberg-Whitham-type equation. By means of a weaker conserved L2-norm, we show some wave-breaking criteria for the equation, which improve some blow-up results on the classical Fornberg-Whitham equation. Moreover, our conclusions suggest that the wave breaking for the equation may occur even with small slope of the initial value. To analyze the interaction between nonlinear and nonlocal dispersion terms, we provide two different approaches. The first one is based on a subtle analysis on evolution of the solution u and its gradient ux. The other is to make full use of the known blow-up results on Riccati-type inequalities with t-dependent functions.