A safe and smooth operating path is a prerequisite for mobile robots to accomplish tasks. Although the existing path optimization methods improve the smoothness of the planned path by introducing Bézier curve to locally optimize the path with regard to turning points, most of these methods manually select the position of control points and subjectively analyze the feasibility of the optimized path. It is argued unfavourably that it exhibits strong subjectivity and cumbersome selection process. To this gap, an adaptive path-smoothening optimization method is proposed in this study, which combines neural network, genetic algorithm, and Bézier curve to effectively resolve the problems of strong subjectivity, cumbersome steps, and thus low efficiency in the selection process of control points. To start with, the data set corresponding to the position of the control point and the path offset are constructed. Based on the actual working conditions, the value space of control point position is derived. Latin hypercube sampling is used to sample the control point position of the second-order Bézier curve, which is input into the Bézier curve solution model to calculate the corresponding path offset. The data set corresponding to the position of control point and path offset are thus acquired. Based on the data set, the neural network algorithm is used to train it, and the prediction model of path offset is constructed. Subsequently, with reference to the prediction model of path offset, a performance evaluation function is formulated by comprehending multiple influential factors of mobile robot motion safety and path smoothness. The genetic algorithm is then introduced to detect the optimal control points in different environments. The proposed method is verified by experiments in different operating environments. The study results show that the currently proposed adaptive path-smoothening optimization method exhibits remarkably superior applicability and effectiveness compared to the currently prevailing methods. It demonstrates advantages of fast path planning, reduced path turning points, and desirable path smoothness. In addition, it can also ensure the safety of mobile robot along the planned path as availed by a pre-set criterion.