We investigate a homopolymer brush system on the basis of the wormlike-chain model, incorporating an Onsager-type interaction between polymer segments in the excluded-volume interaction. The model depends on the ratio between the total polymer length and the persistent length and a reduced grafting density as two basic parameters. Our numerical solutions to the self-consistent field theory are compared with scaling properties that can be deduced in various limits. In the limit of long chain and weak-to-moderate grafting density, our numerical results follow the scaling power law predicted by the classical-trajectory theory of a flexible polymer brush. In the limit of long chain and high grafting density, our numerical results show that the brush properties are comparable to the conformational properties of a nematic wormlike solution. In the limit of rod brush, our numerical results are consistent with the solution of a trial-function treatment from a previous mean-field theory.