In this paper, an approach based on a liquid state machine (LSM) to compute the movement profiles to achieve a gait pattern subject to different variations in its trajectory is presented. At the same time, the position of the zero moment point (ZMP) to determine the stability of the six degrees-of-freedom (6DOF) bipedal robot in the sagittal plane during the gait cycle is calculated. The system is constructed as a supervised machine learning model. The time series of the oscillating foot trajectory obtained by direct kinematics with a multilayer perceptron neural network (MLP), to strengthen the kinematic model, is considered as input values for training. The target movement profiles are acquired of a human gait cycle analysis in three different scenarios: normal gait, climbing stairs, and descending stairs. In training, this model also gets the trajectories of the ZMP position during the gait cycle, as target time series. The LSM formed by spiking neurons, considered as third-generation neural networks, is compared in the accuracy of prediction, by the dynamic time warping (DTW) technique and correlation analysis, against the human gait analysis database. With this neuronal system, the joint positions to generate a trajectory of the oscillating foot and the ZMP position of the bipedal in the sagittal plane in different scenarios are obtained, proving the robustness of the LSM.