In this paper a quadratic curve equating method for different test forms under a random-group data-collection design is proposed. Procedures for implementing this method and related issues are described and discussed. The quadratic-curve method was evaluated with real test data (from two 30-item subtests for a professional licensure examination and two 20-item subtests from the reading portion of the American College Testing program assessment) and simulated data in terms of model fit and equating error, and was compared with several other equating methods. It was found that the quadratic-curve method fit many of the real test data examined, and that when the model fits the population, this method could perform better than other, more sophisticated equating methods. Six tables and 12 figures illustrate the analyses. (Contains 9 references.) (SLD)