Let A be an operator with the polar decomposition A = UIAI. The Aluthge transform of the operator A, denoted by Ā, is defined as Ā = IAI 1 2U IAI 1 2 . In this paper, first we generalize the definition of Aluthge transformfor non-negative continuous functions f; 1 such that f (x)1(x) = x (x - 0). Then, by using this definition, we get some numerical radius inequalities. Among other inequalities, it is shown that if A is bounded linear operator on a complex Hilbert space H, then h (w(A)) - 1 4 h - 12 (jAj) - + h - f 2 (jAj) - + 1 2 h - w - ˜A f;1 - ; where f; 1 are non-negative continuous functions such that f (x)1(x) = x (x - 0), h is a non-negative and non-decreasing convex function on [0;1) and A f;1 = f (IAI)U1(IAI).