Aggregates form 60% to 75% of concrete volume and thus influence its mechanical properties. The strength of normal concrete is affected by the maximum size of a well-graded coarse aggregate by two opposing ways. Concrete mixes containing larger aggregate particles needs less mixing water than those containing smaller aggregates. On the other hand, the smaller size aggregates give larger surface area for bonding with the mortar matrix. This study is a trial to cover these two points with testing three different useable concrete mixes in Kurdistan RegionIraq which are 1:1.5:3, 1:2:4 and 1:3:6 (Cement: Sand: Gravel). In each mix, five maximum aggregate sizes were used which are 9.5mm, 12.5mm, 19mm, 25mm and 37.5mm , the consistency of the all mixes is fixed for slumps of 25-50mm . According to the test results it is concluded that in general the compressive strength of concrete increases when the maximum size of aggregate decreases and the maximum aggregate size strongly influences the concrete strength. Test results also show that the optimum concrete strength is reached by using aggregates of 9.5mm maximum size. We further concluded that for a specified strength, an economical mix can be produced by decreasing the amount of cement and using an appropriate maximum aggregate size.