An approach to design an invisible cloak with controlled constitutive parameters and arbitrary shaped boundaries is presented. Helmholtz's equation is adopted to establish a mapping between original and transformed coordinates inside the cloak. Then the constitutive parameters are obtained by the established mapping. The analytical solution of a regular cloak and the numerical solution of an irregular cloak both verify that that our method will guide electromagnetic wave efficiently and control the constitutive parameters of the cloak conveniently. It has great significance in realizing a cloak practically.