We obtain the Holder continuity and joint Holder continuity in space and time for the random field solution to the parabolic Anderson equation (
t-1/2△)
u=
u◇
W in
d-dimensional space, where
W is a mean zero Gaussian noise with temporal covariance
γ0 and spatial covariance given by a spectral density
μ(
ξ). We assume that
γ0(
t) ≤
c|
t|
-α0 and |
μ(
ξ)| ≤
c|
ξi|
-αi or |
μ(
ξ)| ≤
c|
ξ|
-α, where
αi,
i=1,…,
d (or
α) can take negative value.