A new method based on the Backus-Gilbert approach is proposed to solve the 2-D inverse problem for travel times observed along different ray paths. The unknown velocity function V(x, y) is assumed to be the smoothest, and finite at infinity. In this case it proves to be a solution of the 2-D Poisson's equation. The method is expanded to the case when the data are the phase and/or group surface-wave velocities along different paths, corresponding to different periods. The phase slowness is approximated by a polynomial in the powers of frequency such that the group slowness is also represented by the polynomial of the same power. The coefficients of the polynomial, which are the unknown functions of the coordinates x, y, are estimated by the method mentioned above. The advantage of this approach is that in order to determine phase-velocity distributions, we may use the phase-velocity data for a few of the ray paths and compensate for the lack of information by a large body of the group-velocity data, which are much more easily obtained from observations. The method was tested on a numerical example and applied for interpretation of the phase and group velocities in southeastern Europe.