Optimal k-step, 4- to 10-stage, explicit, strong-stability-preserving Hermite–Birkhoff (SSP HB) methods of order 4 with nonnegative coefficients are constructed by combining linear k-step methods with 4- to 10-stage Runge–Kutta (RK) methods of order 4. These new methods preserve the monotonicity property and prevent the growth of error; therefore, they are suitable for solving hyperbolic PDEs by the method of lines. Moreover, the series of new HB methods have larger effective SSP coefficients and larger maximum effective CFL numbers than Huang’s hybrid methods of the same order and RK methods of the same stage number and the same order when applied to inviscid Burgers’ equations.