We report the results of 87Rb NMR measurements on RbOs2O6, a new member of the family of the superconducting pyrochlore-type oxides with a critical temperature Tc = 6.4 K. In the normal state, the nuclear spin-lattice relaxation time T1 obeys the Korringa-type relation T1T = constant and the Knight shift is independent of temperature, indicating the absence of strong magnetic correlations. In the superconducting state, T1^{-1}(T) exhibits a tiny coherence enhancement just below Tc, and decreases exponentially with further decreasing temperatures. The value of the corresponding energy gap is close to that predicted by the conventional weak-coupling BCS theory. Our results indicate that RbOs2O6 is a conventional s-wave-type superconductor.