We present a statistical study on the interaction between interplanetary coronal mass ejections (ICMEs) and the induced magnetosphere of Venus when the peak magnetic field of the magnetic barrier was anomalously large (>65nT). Based on the entire available Venus Express data set from April 2006 to October 2014, we selected 42 events and analyzed the solar wind parameters, the position of the bow shock, the size and plasma properties of the magnetic barrier, and the position of the ion composition boundary (ICB). It was found that the investigated ICMEs can be characterized with interplanetary shocks and unusually large tangential magnetic fields with respect to the Venus-Sun line. In most of the cases the position of the bow shock was not affected by the ICME. In a few cases the interaction between magnetic clouds and the induced magnetosphere of Venus was observed. During these events the small magnetosonic Mach numbers inside magnetic clouds caused the bow shock to appear at anomalously large distances from the planet. The positions of the upper and lower boundaries of the magnetic barrier were not affected by the ICMEs. The position of the ICB on the nightside was found closer to the planet during ICME passages which is attributed to the increased solar wind dynamic pressure. Key Points Statistical study of the ICME-Venus interaction Analysis of solar wind and magnetic barrier conditions during ICME passages Decreased altitude of the nightside ionosphere during ICME passages