Abrasion resistance is very important in concrete intended for making roads, canals, floors or pavements and it can be defined as the ability of a surface to resist wear due to rubbing. It is tested by grinding the specimen according to the standard procedure and the measurements are done through volumetric loss of the specimen. Abrasion resistance is influenced by many factors such as the type of aggregate, placement, concrete composition, etc. It is desirable that the concrete contains less cement matrix and that this cement matrix achieves as much strength as possible. Cement matrix achieves the highest strength if it consists of a binder without or with small amount of very fine aggregate particles. The purpose of this paper is to examine the influence of these particles on abrasion resistance and compressive strength of concrete. Six concrete mixes were made, which differ in the granulometric composition of the aggregates and the origin of the aggregates. Same type and quantity of the cement and superplasticizer were used in all mixtures with the same water/cement ratio. The workability of the concrete was tested using the slump method. The ultrasound pulse velocity (UPV), density, dynamic modulus of elasticity, compressive strength and abrasion resistance were tested after 28 days of specimens curing. The measured UPV are within the limits of 3989.36 to 4128.44 m/s, which indicates a good quality of concrete. Compressive strengths ranging from 61.6 to 95.6 MPa were achieved. Abrasion resistance was determined by the loss of volume of the specimen in cm3 in an area of 50 cm2, and values from 21.6 to 27.3 cm3/50 cm2 were measured. According to the test results, no harmful effect of very fine aggregate particles on the abrasion resistance of concrete was observed in this investigation. Also, the positive effect of quartz sand on abrasion resistance was confirmed.