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Finite-frequency travel time tomography is a newly developing method. The main procedure in this new method is to compute the traveltime sensitive kernel. The travel time of the same scatterer needs to be used for computing the traveltime sensitive kernel many times. It is a time-consuming task. It is easy and fast to get the travel time from analytic equations in a simple model such as a homogenous or linear velocity media. However, most of the earth models are layered. It is cumbersome to get the travel time from analytic equations. In order to enhance the computation efficiency, we used the table look-up method to compute the finite-frequency travel time sensitive kernel for P-waves in a layered structure model. We chose the AK135 earth model for the velocity model. The table look-up method saved about 50% of the computation time. We enhanced the computation speed by using the table lookup method in the same velocity model, which was very useful for enhancing the computation efficiency for the finite-frequency travel time tomography. [ABSTRACT FROM AUTHOR]