We have calculated the stellar β-decay rate of the important s-process branching point 134Cs based on the state-of-the-art shell model calculations. At typical s-process temperatures (T ∼ 0.2-0.3 GK), our new rate is one order of magnitude lower than the widely used rate from Takahashi and Yokoi (hereafter TY87). The impact on the nucleosynthesis in AGB stars is investigated with various masses and metallicities. Our new decay rate leads to an overall decrease in the 134Ba/136Ba ratio, and well explains the measured ratio in meteorites without introducing the i-process. We also derive the elapsed time from the last AGB nucleosynthetic event that polluted the early solar system to be >28 Myr based on the 135Cs/133Cs ratio, which is consistent with the elapsed times derived from 107Pd and 182Hf. The s-process abundance sum of 135Ba and 135Cs is found to increase, resulting in a smaller r-process contribution of 135Ba in the solar system.