Abstract: The idea of dimensionality reduction is to develop a n-variable objective function onto an α-dense curve which is subsequently transformed into a one-variable function. It can be proved that the global optima of the univariate function can approximate global optima of the original problem. The approximation degree of the approximate solution depends on the density of the n-dimensional space filled by the curve. When the point on the α-dense curve is in the feasible domain, an approximate solution with sufficient accuracy can be obtained. In some cases, the reducing dimension technology is combined with other algorithms with the aim to explore a new way towards the global optimization. When α-dense curve h is constructed in the feasible set X, a n-dimensional function can be approximated by a one-dimensional function. With increase in the numbers of independent variables, solving the global optima of multivariate function turns to be more complicated and needs more calculations. In order to minimize computational complexity, length of the α-dense curve was computed to obtain general classes of reducing transformations having minimal properties, and the properties of dimensionality reduction need to be investigated. A global optimization approximation algorithm based on dimensionality reduction method was proposed to solve the nonlinear global optimization problem with box constraints. Firstly, a new reduction transformation was constructed on the interval 0, π, and the density of the α-dense curve was given. Secondly, the amount of calculation according to the approximate algorithm was estimated from the length of the α-dense curve and the proof was given. Thirdly, a theoretical algorithm was proposed. Finally, the results of numerical experiments were listed to show the effectiveness of the algorithm.