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In this paper, by using the cosine family theory, measure of non-compactness, the Mönch fixed point theorem and the method of estimate step by step, we establish the existence theorems of mild solutions for fractional impulsive integro-differential evolution equations of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>β</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula> with nonlocal conditions in Banach spaces under some weaker conditions. The results obtained herein generalizes and improves some known results. Finally, an example is presented for the demonstration of obtained results.