In this paper, we show that groups of order $2^npq$, where p, q are primes of the from $p=2^n-1$, $q=2^{n-1}+p$ with $n{geq}3$, are not simple and groups of order $2^npq^t$ for $t{geq}2$, where p, q are odd primes of the form $p=2^m-1$, $q=2^n-1$ with m < n, are not simple.