Synthetic paper with multi-layer structure and excellent printing property

A synthetic paper with a multi-layer structure comprising a biaxially stretched film of an olefinic polymer having a melting point from 130.degree. C. to 210.degree. C. as determined from the peak temperature of the Differential Scanning Calorimetry curve containing from 5 to 40% by weight inorganic fine powders having a mean particle size of from 0.01 to 10 .mu.m as a base material layer (A) having adhered to at least one surface thereof a uniaxially stretched layer (B) having a surface roughness Ra of from 0.3 to 1.5 .mu.m, with the uniaxially stretched layer (B) comprising an .alpha.-olefin propylene copolymer or a high-density polyethylene having a melting point, the peak temperature of the Differential Scanning Calorimetry curve, of from 120.degree. C. to 160.degree. C. which is at least 5.degree. C. lower than the melting point of the olefinic polymer of the base material layer (A), and from 8 to 65% by weight inorganic fine powders having a mean particle size of from 0.01 to 5 .mu.m, wherein the surfaces of the inorganic fine powders contained in the uniaxially stretched layer (B) are coated with the .alpha.-olefin propylene copolymer or the high-density polyethylene, and wherein the surface of the uniaxially stretched layer (B) has a gloss, measured at an angle of 75.degree. of less than 20% and a Bekk Index smoothness of less than 500 seconds.