© 2021, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.In this work, the numerical solutions of advection-diffusion equation are investigated through the finite element method. The quartic-trigonometric tension (QTT) B-spline which presents advantages over the well-known existing B-splines is adapted as the base of the numerical algorithm. Space integration of the model partial differential equation is achieved through QTT B-spline Galerkin method. The resultant system of time-dependent differential equations is integrated using the Crank-Nicolson technique. The stability of the current scheme is accomplished and proved to be unconditionally stable. Simulation of several sample problems are carried out for verification of the proposed numerical scheme. Solutions obtained by numerically computed scheme are compared to the existing literature.