A new forward kinematic analysis is proposed to describe the motion of a reptile-like four-legged walking robot using a new dimensionality-reduction method. The three standing legs (assuming one leg is swinging) contain nine driven joints. Only six of these joints, however, are independently driven joints. The remaining joints are redundant driven joints. Finding the redundant driven joint angles has been a key problem in improved forward kinematic analysis of a reptile-like forward kinematic analysis. Solving the associated high-order equation, which is derived using the analytic method, is problematic and slow. In this paper, we use a new dimensionality reduction method to solve this problem. First, we deduced the formulas for the redundant driven joint angles. Then, one of the formulas is transformed to take into account the constraint condition. We then use iteration to find solutions for the remaining equations that satisfy the constraint condition. With the help of MATLAB, a solving system for the forward kinematic analysis of this robot is introduced. Our results show two improvements over the conventional method: shorter computation time and higher precision.