The accelerated failure time partial linear model allows the functional form of the effect of covariates to be possibly nonlinear and unknown. We propose to approximate the nonparametric component by cubic B-splines and construct a Gehan estimating function similar to that under the AFT model. Due to its non-smoothness, which will lead to computational challenge in estimating standard error, we propose a polynomial-based smoothing Gehan estimating function and compute the estimate of the parameters involved using the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Asymptotic properties of the resulting estimators are established. The proposed method presents a good performance in the simulation studies and is applied to two real data sets.