This article has explored a hybrid numerical approach in analysis of the Burgers equation with involving steep gradients. The technique is based on a quadratic B-spline finite element method in strong form for space variation. This paper discovers how to find an α-family optimization approach for temporal variations. The proposed method has been shown to be unconditionally stable for 𝛼≥0.5. Yet, the efficiency of the proposed scheme on relatively coarse grids has been demonstrated. The numerical illustrations show that the present method has been seen to be more accurate than the literature and effectively captures the shock behaviours.