We study the decay rate of large deviation probabilities of occupation times, up to time t, for the voter model eta : Z(2) x [0, infinity) -> {0, 1} with simple random walk transition kernel, starting from a Bernoulli product distribution with density rho is an element of (0, 1). In [Probab. Theory Related Fields 77 (1988) 401-413], Bramson, Cox and Griffeath showed that the decay rate order lies in [log(t), log(2)(t)].