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This paper deals with the approximate controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space. We delete the compactness condition or Lipschitz condition for nonlocal term appearing in various literatures, and only need to suppose some weak growth condition on the nonlocal term. The discussion is based on the fixed point theorem, diagonal argument and approximation techniques. In the end, an example is presented to illustrate the abstract theory. [ABSTRACT FROM AUTHOR]