Since proposed by NSA in June, 2013, SIMON and SPECK families have attracted the attention of massive cryptographers. More recently, at CHES 2015, a lightweight block cipher Simeck is proposed, which has adopted the merits from both SIMON and SPECK. However, the security level on Simeck against integral cryptanalysis has never been evaluated. This paper firstly proposes some theoretical and experimental integral distinguishes on Simeck. More specifically, 12/14/16-round theoretical integral distinguishers on Simeck32/48/64 and some 15-round experimental integral distinguishers on Simeck32 are firstly presented. With these integral distinguishers, Simeck32/48/64 reduced to 21/21/24 rounds respectively can be attacked with integral cryptanalysis.