In this paper, we study the multiplicity of solutions with a prescribed L2-norm for a class of nonlinear Kirchhoff type problems in 2250ef231f81c944b726d55320ed5" title="Click to view the MathML source">R3iv class="formula" id="fd000005">iv class="mathml">−(a+b∫R3|∇u|2)Δu−λu=|u|p−2u,iv>iv> where a,b>0 are constants, λ∈R, . To get such solutions we look for critical points of the energy functional iv class="formula" id="fd000010">iv class="mathml">iv>iv> restricted on the following set iv class="formula" id="fd000015">iv class="mathml">iv>iv> For the value considered, the functional Ib is unbounded from below on Sr(c). By using a minimax procedure, we prove that for any c>0, there are infinitely many critical points of Ib restricted on Sr(c) with the energy . Moreover, we regard b as a parameter and give a convergence property of as b→0+.