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A novel adaptive algorithm for a second order adaptive lattice notch filter is represented. It is established based on a robust variable step-size plain gradient algorithm (VSPG) and the proposed time-varying notch bandwidth technique. This technique can improve the convergence speed of the VSPG up to many times. The time-varying notch bandwidth is adjusted to be wide when the algorithm is far from the optimum. As algorithm approaches the optimum, the notch bandwidth is automatically adjusted to be narrow. In the early stage of adaptation, the proposed algorithm has high speed due to the wide bandwidth while ensuring high accuracy in the desired parameter due to the final narrow bandwidth. Extensive simulations are provided to show the performances of the novel adaptive algorithm. In addition, the coefficient bias and mean square error (MSE) are also revealed.