We compute the quantum cohomology ring $\mathrm {QH}^*_\varphi (\mathbb {P}_\Sigma ,\mathbb {C})$ of an arbitrary $d$-dimensional smooth projective toric manifold $\mathbb {P}_\Sigma $ associated with a fan $\Sigma $. The multiplicative structure of $\mathrm {QH}^*_\varphi (\mathbb {P}_\Sigma ,\mathbb {C})$ naturally depends on the choice of an element $\varphi $ in the ordinary cohomology group $\mathrm {H}^*(\mathbb {P}_\Sigma ,\mathbb {C})$. We check several properties of the quantum cohomology rings $\mathrm {QH}^*_\varphi (\mathbb {P}_\Sigma ,\mathbb {C})$ which are supposed to be valid for quantum cohomology rings of a wide of Kähler manifolds.