This paper will study global adaptive control for a class of multi-input non-linearly parameterized systems. The systems are assumed to be in interlaced form, which include a single-input nonlinearly parameterized systems as a special case. Our proposed adaptive controller is a switching-type controller, in which the gain parameter is tuned online via a switching scheme. In our proposed switching scheme, the switching time is finite and the gain parameter is eventually constant. An example is given to show the effectiveness of the proposed controller.