This paper studies the tracking control problem for a climate chamber control system used for determining volatile organic compounds. A new nonlinear controller, for the first time, is designed for the temperature and humidity control of a 300.33emm3$30\text{ m}^3$ climate chamber. For one thing, based on the backstepping technology, an improved control method is proposed with the help of the implicit function theorem instead of employing system linearization. In this way, simplification of the controlled system can be avoidable so that the control accuracy is promoted. For another, without approximations by fuzzy logics or neural networks, the number of complex computations are reduced a lot so that the control rate is improved considerably. In the end, simulation is conducted by Matlab to validate the effectiveness and superiority of the proposed control method.