A guarded cylindrical graphite ionization chamber of nominal volume 1000 cm³ was designed and fabricated for use as a reference standard for low-dose rate ¹³⁷Cs brachytherapy sources. The air kerma calibration coefficient (N_K) of this ionization chamber was estimated analytically using Burlin’s general cavity theory, as well as by the Monte Carlo simulation and validated experimentally using Amersham CDCS-J-type ¹³⁷Cs reference source. In the analytical method, the N_K was calculated for 662 keV gamma rays of ¹³⁷Cs brachytherapy source. In the Monte Carlo method, the geometry of the measurement setup and physics-related input data of the ¹³⁷Cs source and the surrounding material were simulated using the Monte Carlo N-Particle code. The photon energy fluence was used to arrive at the reference air kerma rate (RAKR) using mass energy absorption coefficient. The energy deposition rates were used to simulate the value of charge rate in the ionization chamber, and the N_K was determined. The analytical and Monte Carlo values of NK of the cylindrical graphite ionization chamber for ¹³⁷Cs brachytherapy source are in agreement within 1.07%. The deviation of analytical and Monte Carlo values from experimental values of  N_K is 0.36% and 0.72%, respectively. This agreement validates the analytical value, and establishes this chamber as a reference standard for RAKR or AKS measurement of ¹³⁷Cs brachytherapy sources.