Abstract: This paper discusses the following quadrature rule with higher degree of accuracy ∫_a^bf(x)dx)=(b-a)(7f(a)+16f((a+b)/(2))+7f(b)+(b-a)(f'(a)-f'(b)))/30+E[f] Where E[f]=((b-a)⁷/(604800))f⁽⁶⁾(ξ),a<ξ<b andits Compositrule are presented aswell:∫_a^b(f(x)dx)=(b-a)((7f(a+2ih)+7???19880410-2???f(a+2ih)+16f(a+2i-1h)+(b-a)(f'(a)-f(b))/2n)/30n+E_n[f] Where E_n[f]=((b-a)⁷)/(604800n⁶)f⁽⁶⁾(η),a< η< b h=(b-a)/2n which possess the all advantages of simpsons rule, but the degree of accuracy isincreased by two order than Simpson's rule.The numerical tests that the quadrature formula of this paper is very efficient.