ABSTRACT.We discuss the notion of Pythagorean subbisemiring, level sets of Pythagorean subbisemirings and Pythagorean normal subbisemiring of a bisemiring and investigate some of the properties related to subbisemirings. The fuzzy subset \[L = (\mu_{S}^{P}, \, \omega_{S}^{P})\]is a Pythagorean subbisemiring if and only if all non-empty level set \[L_{(\alpha,\beta)} \, (\alpha,\beta \in (0,1])\]is a subbisemiring. The Cartesian product of two Pythagorean subbisemirings is also Pythagorean subbisemiring. The homomorphic image and preimage of Pythagorean subbisemiring is also Pythagorean subbisemiring. To illustrate our results and examples are given.