We consider a restricted planar circular three-body problem (Sun-Jupiter-asteroid) in a non-resonance case. There are two new algorithms developed for construction of a quasi-periodic solution in a trigonometric form by means of computer algebra. The first corresponds to classical method of simple iterations leading to series in powers of small mass mJ, the second, to iterations with rapid (quadratic) convergence, but having ordinary type and not involving a successive coordinate transformations. All these iterations require a realization of algebraic operations on trigonometric polynomials with the help of computers of high capacity. It would be interesting to compare the solutions obtained with the two algorithms and to estimate the domain of their practical convergence.