In this paper we shall prove some weighted norm inequalities of the form $${int}_{R^n};|Tf(x)|^pu(x)dx;{leq};C_p;{int}_{R^n};|f(x)|^pNu(x)dx$$ for certain rough singular integral T and maximal singular integral $T^*$. Here u is a nonnegative measurable function on $R^n$ and N denotes some maximal operator. As a consequence, some vector valued inequalities for both T and $T^*$ are obtained. We shall also get a boundedness result of T on the Triebel-Lizorkin spaces.