Let D be the unit disc and H(D) be the set of all analytic functions on D. In [2], C. Cowen defined a space H = { f ∈ H ( D ) : F ( z ) = ∑ k = 0 ∞ a k ( z + 1 ) k , ∀ z ∈ D , ∥ f ∥ 2 = ∑ k = 0 ∞ | a k | 2 4 k < ∞ } In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied.