In this paper, we construct a new efficient numerical scheme for variable fractional order differential equation of fourth order with delay. Here, we propose to use parametric quintic spline in the spatial dimension and L 2 − 1 σ formula for time dimension. The stability, convergence, and solvability are rigorously proved using discrete energy method. Our proposed scheme improves convergence in both aspects (spatial-dimension and time-dimension) in comparison to those earlier work. Numerical simulation is carried out using the MATLAB software to demonstrate the effectiveness of our scheme. [ABSTRACT FROM AUTHOR]