We obtained a wide-band spectrum of the Compton-thick Seyfert 2 galaxy Mrk 3 with Suzaku. The observed spectrum was clearly resolved into weak, soft power-law emission, a heavily absorbed power-law component, cold reflection, and many emission lines. The heavily absorbed component, absorbed by gas with a column density of 1.1x10^24 cm^-2, has an intrinsic 2--10 keV luminosity of ~1.6x10^43 erg s^-1, and is considered to be direct emission from the Mrk 3 nucleus. The reflection component was interpreted as reflection of the direct light off cold, thick material; the reflection fraction $R$ was 1.36+/-0.20. The cold material is inferred to be located > 1 pc from the central black hole of Mrk 3 due to the low ionization parameter of iron (xi < 1 erg cm s^-1) and the narrow iron line width (s < 22 eV). A Compton shoulder to the iron line was detected, but the intensity of the shoulder component was less than that expected from spherically distributed Compton-thick material. The weak, soft power-law emission is considered to be scattered light by ionized gas. The existence of many highly-ionized lines from O, Ne, Mg, Si, S, and Fe in the observed spectrum indicates that the ionized gas has a broad ionized structure, with xi=10--1000. The scattering fraction with respect to the direct light was estimated to be 0.9+/-0.2%, which indicates that the column density of the scattering region is about 3.6x10^22 cm^-2. This high-quality spectrum obtained by Suzaku can be considered a template for studies of Seyfert 2 galaxies.