Pisier introduced the concept of similarity degree to attack the problem of Dixmier's similarity problem and Kadison's similarity problem in the same context. In this talk we will explain Pisier's similarity degree for completely contractive Banach algebras and apply to the case of Fourier algebra A(G). We will show that for infinite QSIN groups (containing amenable or discrete groups) the similarity degree of the corresponding Fourier algebra is exactly 2. As a consequence we prove the following Fourier algebra version of Dixmier's similarity problem: any cb-homomorphism from A(G) to B(H) is similar to *-representation.