The continuity of Lyapunov exponent plays an important role for many problems in quasi-periodic cocycles. One example is Ten Martini problem. It is well known that the Lyapunov exponent is continuous in analytic topology and discontinuous in C^0-topology. In this talk, we will provide quasi-periodic cocycles at which the Lyapunov exponent is not continuous in C^l-topology with 0 ≤ l ≤ +∞. This is joint work with Jiangong You.