In this study, a new seismic isolation system, based on pendulum behavior, has been introduced and proposed. The system comprising two orthogonal pairs of saddle-stirrups pendulums (SSPs), of specific shape, is proposed in which each SSP has a horizontal upper part that can roll slightly on a flat seat and two vertical hanging stirrup-wise parts that can have pendulum motion, associated with the rolling motion of the upper horizontal part. This way, a kind of pendulum motion-based seismic isolation system is created with a natural oscillation period, which can be easily increased to 2 seconds or more by adjusted an appropriate length of the hanging parts of the SSP, and as a result, the input acceleration to the building is remarkably decreased. To evaluate the system’s performance and efficiency, after a set of finite element analyses for making sure about the appropriate load bearing conditions of system’s parts, the equation of motion of a single-degree-of-freedom (SDOF) system, equipped with the proposed isolator, was derived, based on Lagrange method, considering pendulums’ geometric nonlinearity, and solved numerically, by Runge-Kutta-Nystrom technique, using the MATLAB platform. Several accelerograms of low-, mid- and high-frequency earthquakes were considered, and the seismic responses of isolated and non-isolated SDOF systems, including the maximum drift and maximum absolute acceleration, were compared. For verification of the formulation and the MATLAB code, developed by the authors for the nonlinear time history analysis (NLTHA), three cases were considered. In the first case, the isolated system response to a sinusoidal input with the initial frequency of the system was obtained and checked against the response values obtained by using the exact solution. In the second case, the length of the pendulum was assumed to be very large, resulting in a very long period of the isolated system, so that its absolute acceleration response approached zero, and its relative displacement response became almost the negative values of the ground displacement at each time instant. In the third case, a very short length, almost zero, was considered for the pendulum, and the isolated system responses were very close to those of non-isolated system, as expected. Results of conducted series of NLTHA show that the proposed SSP isolation system reduces the maximum values of absolute acceleration, base shear, and story drift of the buildings around 70% on average. Results also show that the maximum displacement above the isolation level is around 40 cm, on average, and decreases with increasing the pendulum length from 2.0 m to 3.0 m. Based on the structure and the main components of the proposed SSP isolator, and the obtained numerical results, it can be claimed that the SSP isolator is a low-tech low-cost type seismic isolator with high efficiency in response reduction of buildings. As such its application in short to medium buildings can be strongly recommended, particularly in underdeveloped and developing, and even developed countries, located in seismic regions. For application of the proposed system in relatively tall building further studies are required, which are presently at hand by the authors, and would be accomplished hopefully soon.