In this paper, we study spherical Hecke algebras of SL₂ over two dimensional local fields. In order to define the convolution product, we make explicit use of coset decompositions. We also consider spherical Hecke algebras of the torus of SL₂ and construct the Satake isomorphism between two spherical Hecke algebras. In order to define the Satake isomorphism, we use the invariant measure on two-dimensional local fields with values in R ((X)) constructed by I. Fesenko