Direct laser acceleration (DLA) of electrons can be achieved by utilizing the axial field of a well-guided, radially polarized laser pulse in a density-modulated plasma waveguide. When a laser pulse of a few terawatt (TW) peak power is applied, however, the laser ponderomotive force perturbs plasma electrons to concentrate in the center, such that the generated electrostatic fields can significantly defocus the externally injected electron witness bunch and considerably deteriorate the acceleration efficiency. To improve the performance of DLA, a leading electron bunch, which acts as a precursor, can be introduced in DLA to effectively confine the witness bunch. Three-dimensional particle-in-cell simulations have been conducted to demonstrate that the transverse properties of the witness bunch can be significantly improved when a precursor bunch is used. Selected bunch transverse sizes, bunch charges, and axial separation from the witness bunch have been assigned to the precursor in a series of DLA simulations. Since a favorable ion-focusing force is provided by the precursor, the transverse properties of witness bunch can be maintained when a relatively high-power (∼2 TW) laser pulse is used in DLA, and an improved overall acceleration efficiency can be achieved.