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In this paper,the authors investigate the optimal conversion rate at which land use is irreversibly converted from biodiversity conservation to agricultural production.This problem is formulated as a stochastic control model,then transformed into a HJB equation involving free boundary.Since the state equation has singularity,it is difficult to directly derive the boundary value condition for the HJB equation.They provide a new method to overcome the difficulty via constructing another auxiliary stochastic control problem,and impose a proper boundary value condition.Moreover,they establish the existence and uniqueness of the viscosity solution of the HJB equation.Finally,they propose a stable numerical method for the HJB equation involving free boundary,and show some numerical results.