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This study reports the experimental work undertaken to investigate the optimum grading of limestone to be used in concrete mixes. 36 concrete cubes were prepared for testing. Four different Fineness Moduli and grading were tested 2.4, 2.6, 2.92 and 3. For all tests, the cubes were left in curing until testing at the age of 3, 7 and 28 days respectively. Samples were loaded to failure and the average compressive strength was used for comparison purposes. Flow table test has been performed on the fresh concrete directly after mixing to measure workability and the average of the maximum concrete spread parallel to the two edges of the table was recorded. Results revealed that the optimum Fineness Modulus for the limestone to be used as fine aggregate in the concrete mix to get maximum compressive strength is 2.78. The flow table tests revealed an increment in the workability of fresh concrete with higher Fineness Modulus of limestone used in the concrete mix as fine aggregate. The workability of the optimum Fineness Modulus, 2.78, was found to be 412 mm which is a mix with considerable workability. An ideal grading has been recommended in this research study and checked to match the ASTM grading requirements for fine aggregate.