In this paper, we consider the following Schrödinger equations with critical growthwhere N ≥ 4, 2 * is the critical Sobolev exponent, a(x) ≥ 0 and its zero sets are not empty, λ > 0 is a parameter, δ > 0 is a constant such that the operator (− + λa(x) − δ) might be indefinite for λ large. We prove that if the zero sets of a(x) have several isolated connected components 1 , · · · , k such that the interior of i (i = 1, 2, . . . , k) is not empty and ∂ i (i = 1, 2, . . . , k) is smooth. Then for λ sufficiently large, the equation admits, for any i ∈ {1, 2, · · · , k}, a solution which is trapped in a neighborhood of i . The key ingredients of the paper are using a flow argument and a combination of global linking and local linking.