Let $${{\cal D}_{\lambda ,\mu }}$$ be the space of linear differential operators on weighted densities from $${{\cal F}_\lambda }$$ to $${{\cal F}_\mu }$$ as module over the orthosymplectic Lie superalgebra $$\mathfrak{osp}(3\left| 2 \right.)$$ , where $${{\cal F}_\lambda }$$ , $$\lambda \in \mathbb{C}$$ is the space of tensor densities of degree λ on the supercircle S1∣3. We prove the existence and uniqueness of projectively equivariant quantization map from the space of symbols to the space of differential operators. An explicite expression of this map is also given.