As a freehand curve recognition method for sketch-based CAD systems, we previously proposed the Fuzzy Spline Curve Identifier (FSCI), which identifies a freehand curve as one of seven types of primitive geometric curve based on the drawing style of the user and the curve shape. Moreover, we have realized a trainable version of FSCI in which the identification characteristics can be tuned according to each user's drawing data by the back-propagation learning algorithm. However, users are required to draw a considerable number of primitive geometric curves to collect enough drawing data to tune the FSCI before starting practical drawing on a sketch-based CAD system. The present paper proposes an on-line training mechanism for FSCI in which its identification characteristics are adaptively and automatically tuned while a user is operating the sketch-based CAD system.