In this paper, the authors presented a novel experimental strategy and its computational scheme to determine line tensions of solid-liquid systems from the shape of axisymmetric liquid-vapor interface profiles around a conic cylinder. In this method, a carefully prepared conic cylinder was inserted vertically into a tested liquid. The capillary rise profile and the shape of the cylinder were digitized by applying computer image processing and analysis techniques. A data processing scheme was developed to calculate the local angle of inclination of the conic cylinder surface and the radius of the three-phase contact circle. The contact angle, as an adjustable parameter, was found by numerically minimizing the discrepancy between the theoretical Laplacian curve and the physically observed liquid-vapor interface profile. The measured contact angles increased by approximately 4 degrees to 6 degrees as the term cos beta/R(c), representing the line tension effect, increased from approximately -2.0 to 10.0 cm(-1). This was then interpreted in terms of line tension by the modified Young equation for the three-phase line in contact with an inclined solid surface. Line tensions of four n-alkane liquids on the FC725 surface were determined by using this new experimental technique. The measured line tensions were positive and of the order of 1 mu J/m for all the four solid-liquid systems in our study. These results are consistent with the published data for similar solid-liquid systems obtained by the axisymmetric drop shape analysis technique. In comparison with the sessile drop method, this method has an additional adjustable parameter, the inclined angle, which allowed us to study the line tension effect in a much larger range.