A method of 3D traveltime tomography that uses the data on the travel time residuals of body waves is suggested. The underlying assumption of the method is smooth horizontal variations of the velocity. The studied domain is divided into layers, and the velocity correction in each layer is assumed to only depend on the horizontal coordinates. The initial velocity model is specified as a certain depth distribution of the velocity. The numerical implementation of the method is noticeably simpler if the initial distribution is described by a linear function. The solution is based on minimizing the functional that contains the sum of the integrals of the square gradients of the velocity corrections. The procedure reduces to solving the two-dimensional (2D) problem in a way similar to that previously developed for the surface wave tomography (Ditmar and Yanovskaya, 1989). The obtained solution is smoothed, and the degree of smoothing is determined simultaneously with the reconstruction of the solution. This approac