Complex traveltime of seismic wave plays an important role in dealing with caustics with which geometric ray theory faces.To obtain a higher accuracy and a more efficient method for calculating the complex traveltime,the authors introduce the L-BFGS optimization method to calculate the imaginary slowness.In addition,orthogonal condition of the real part and imaginary part of complex traveltime are taken as the objective function,and then a new L-BFGS-FMM method is obtained for computing complex traveltime.The numerical examples demonstrate the effectiveness of L-BFGS-FMM used in this paper.An analysis of accuracy and efficiency of the results obtained by using the analytical method,dynamic ray tracing method,Gauss-Newton-conjugate gradient method and L-BFGS-FMM method shows that the L-BFGS-FMM method introduced in this paper is superior to all the other methods,and hence the method introduced in this paper can meet the large-scale computing requirement in practical applications.