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We introduce a numerical solution of the inverse light-scattering problem for a single non-absorbing spherical particle. The solution is implemented by global optimization at preliminary constructed database of light-scattering patterns. We propose an adaptive method for database construction, which aims both at providing satisfactory local accuracy and at avoiding large errors of the inverse map. Several databases were constructed varying the required accuracy of solution of the inverse problem and parameters used to characterize a sphere. We tested accuracy of the method on synthetic data for spheres with and without noise, on synthetic data for slightly prolate and oblate spheroids, and on experimental data of polystyrene microspheres measured with a scanning flow cytometer. The constructed databases have shown appropriate results in determination of the size and refractive index of a sphere from the angle-resolved light scattering with given accuracy.