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In this paper we study the Chen–Ruan cohomology ring of weighted projective spaces. Given a weighted projective space 
${{\mathbf{P}}^{n}}_{{{q}_{0}},\ldots ,{{q}_{n}}}$, we determine all of its twisted sectors and the corresponding degree shifting numbers. The main result of this paper is that the obstruction bundle over any 3-multisector is a direct sum of line bundles which we use to compute the orbifold cup product. Finally we compute the Chen–Ruan cohomology ring of weighted projective space 
$\mathbf{P}_{1,\,2,\,2,\,3,3,\,{{3}^{\centerdot }}}^{5}$.
