  Most fully developed galaxies have a vivid spiral structure, but the
formation and evolution of the spiral structure are still an enigma in
astrophysics. In this paper, according to the standard Newtonian gravitational
theory and some observational facts, we derive an idealized model for spiral
galaxy, and give a natural explanation to the spiral structure. We solve some
analytic solutions to a spiral galaxy, and obtain manifest relations between
density and speed. From the solution we get some interesting results: (I) The
spiral pattern is a stationary or static structure of density wave, and the
barred galaxy globally rotate around an axis at tiny angular speed. (II) All
stars in the disc of a barred spiral galaxy move in almost circular orbits.
(III) In the spiral arms, the speed of stars takes minimum and the stellar
density takes maximum. (IV) The mass-energy density of the dark halo is
compensatory for that of the disc, namely, it takes minimum in the spiral arms.
This phenomenon might reflect the complicated stream lines of the dark halo.
