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

*γ*_{0} and spatial covariance given by a spectral density

*μ*(

*ξ*). We assume that

*γ*_{0}(

*t*) ≤

*c*|

*t*|

^{-α0} and |

*μ*(

*ξ*)| ≤

*c*|

*ξ*_{i}|

^{-αi} or |

*μ*(

*ξ*)| ≤

*c*|

*ξ*|

^{-α}, where

*α*_{i},

*i*=1,…,

*d* (or

*α*) can take negative value.