The emergent education of young children's self-invented music notations has been frequently neglected. The past studies have documented that young children can invent notations to record music although they can not read traditional music notation. This study was designed to guide young children to invent to music notations by teaching them the music elements of pitches and durations. Through the analysis of collected materials of children's writings, this study aimed to investigate young children's self-invented music notations. The result found that children's self-invented music notations include geometrical patterns and borrowing symbols. Furthermore, the geometrical patterns of notating pitches were subdivided into two classifications according to the hierarchical relation was shown or not. On the other hand, the geometrical patterns of notating durations were subdivided into two classifications according to the beat unit was shown or not. While the geometrical patterns of notating pitches were belonged to the classification of hierarchical relation, the relative position of pitch was indicated. While the geometrical patterns of notating durations were belonged to the classification of beat unit, the relative duration to beat was indicated. The self-invented music notations of the relation between pitches or durations reflect children's music cognition.