Abstract: A new method of linear summation of double Fourier series was put forward on a parallel hexagon associated with 3directional partition. A specific summation factor was so constructed that an integral operator with the summation factor converged uniformly to any given continuous function with periodic domain Ω, where Ω is a parallel hexagon domain. Furthermore, the convergence order of the operator was presented for the smooth approached function.

Key words: double Fourier series, summation factor, threedirection coordinate, parallel hexagon domain, convergence