Speed, accuracy, and flexibility are crucial to the practical use of on - line handwriting recognition. Besides, extensibility is also an important concern as we move from one domain to another which requires the character set to be extended. This research, produce a study for simple yet robust structural approach for recognizing on - line handwriting. In this approach is designed to achieve reasonable speed, high accuracy and sufficient tolerance to variations. At the same time, it maintains a high degree of reusability and hence facilitates extensibility. Experimental for study results show that the recognition rates are 98.60% for digits, 98.49% for the uppercase letters, 97.44% for lowercase letters, and 97.40% for the combined set. When the rejected cases are excluded from the calculation, the rates can be increased to 99.93%, 99.53%, 89.55% and 98.07%, respectively. Keywords: Structure extraction, structural primitives; Flexible structural matching, and On-line handwritten character recognition.