The objective of this study is to develop a triad problem-solving model of design with a controllable determinization level which satisfies both analytic and synthetic aspects of design activities. Rooted on the problem-solution duality model, a goal-oriented triad problem-solving model, which is based on the triad relationship among a problem, a solution, and a goal, is constructed. The goal area is distinguished from the solution area. The concept of determinization which is the process of transforming the indeterminate solution area into the quasi-determinate2 goal area is established. The determinization level controls the portion between discovery and invention. The triad problem-solving model of design with a controllable determinization level is applicable to all types of design activities with diverse conditions.