To date, various paradigms of soft-Computing have been used to solve many modern problems. Among them, a self organizing combination of fuzzy systems and neural networks can make a powerful decision making system. Here, a Dynamic Growing Fuzzy Neural Controller (DGFNC) is combined with an adaptive strategy and applied to a 3PSP parallel robot position control problem. Specifically, the dynamic growing mechanism is considered in more detail. In contrast to other self-organizing methods, DGFNC adds new rules more conservatively; hence the pruning mechanism is omitted. Instead, the adaptive strategy 'adapts' the control system to parameter variation. Furthermore, a sliding mode-based nonlinear controller ensures system stability. The resulting general control strategy aims to achieve faster response with less computation while maintaining overall stability. Finally, the 3PSP is chosen due to its complex dynamics and the utility of such approaches in modern industrial systems. Several simulations support the merits of the proposed DGFNC strategy as applied to the 3PSP robot.