The computability of the solution operator of the Cauchy problem for the nonlinear Davey-Stewartson equation is studied in this paper. Firstly, a nonlinear map KRH5(R2)→C(R;H5(R2)), where H5(R2) is inhomogeneous Sobolev space on R2, defined from the initial value Φ to the solutionu. Then we used the relevant knowledge of type-2 theory of effectivity, functional analysis and Sobolev space to prove that when s>4/7 the solution operator of the Cauchy problem for the nonlinear Davey-Stewartson equation is computable. The conclusion enriches the theories of computability.