Antiscatter grid made from glass capillaries was proposed by our group in 1991. Now several tens grids for mammography have been made. Preliminary results of investigation of such a grid are published for the first time. Further development of the capillary grid production technology will allow to decrease sharply the patient dose, and to obtain a high contrast image of the object under investigation. Experimental results of measurement the capillary grid's parameters in comparison with the same parameters of the commercial antiscatter grids are presented.