Objective. The variable flip angle (VFA) method for longitudinal relaxation time (T-1) measurement is inherently sensitive to inaccuracies in the radiofRequency transmit field (B-1) and incomplete spoiling of transverse magnetization. The objective of this study is to devise a computational method that addresses the problems of incomplete spoiling and B-1 inhomogeneity in the estimation of T-1 using VFA method. Approach. Using an analytical expression of the gradient echo signal with account of incomplete spoiling, we first showed that ill-posedness in the simultaneous estimation of B-1 and T-1 can be lifted with the use of flip angles larger than the Ernst angle. We then devised a nonlinear optimization method based on this signal model of incomplete spoiling for simultaneous estimation of B-1 and T-1. Main results. We evaluated the proposed method on a graded-concentration phantom to show that the derived T-1 estimates offers an improvement over the regular VFA method and compares well with reference values measured by inversion recovery. Reduction of the number of flip angles from 17 to 5 yielded consistent results indicating that the proposed method is numerically stable. T-1 estimates derived from in-vivo brain imaging were consistent with literature values for gray and white matter tissues. Significance. Contrary to the common notion that B-1 correction in the VFA method for T-1 mapping should be performed separately, we show that combined estimation of B-1 and T-1 is feasible by the proposed method simply with the acquisition of 5 flip angles, as demonstrated on both phantom and in-vivo imaging data.