  Finite temperature SU(3) gauge theory is studied on anisotropic lattices
using the standard plaquette gauge action. The equation of state is calculated
on $16^{3} \times 8$, $20^{3} \times 10$ and $24^{3} \times 12$ lattices with
the anisotropy $\xi \equiv a_s / a_t = 2$, where $a_s$ and $a_t$ are the
spatial and temporal lattice spacings. Unlike the case of the isotropic lattice
on which $N_t=4$ data deviate significantly from the leading scaling behavior,
the pressure and energy density on an anisotropic lattice are found to satisfy
well the leading $1/N_t^2$ scaling from our coarsest lattice, $N_t/\xi=4$. With
three data points at $N_t/\xi=4$, 5 and 6, we perform a well controlled
continuum extrapolation of the equation of state. Our results in the continuum
limit agree with a previous result from isotropic lattices using the same
action, but have smaller and more reliable errors.
