Abstract: Considering a (2n + 2)-polygon P, a geometric realization was proposed for cluster algebra \mathcalB of type B. As an application, a cluster expansion formula was presented for each cluster variable of \mathcalB and the relationship between clusters of \mathcalB and triangulations of P were clarified. At the same time, the correspondence between orbit flips of \sigma -invariant triangulations \varGamma and mutations of clusters of \mathcalB was constructed based on a designed commutative diagram.