A single, closed three-state ΛΛ-system in room-temperature rubidium is investigated experimentally using a copropagating beam parallel-polarization configuration under weakly driven electromagnetically induced transparency (EIT) condition. Compare with the widely used orthogonal-polarization beam EIT configuration where multiple nonclosed ΛΛ-schemes coexist, the parallel-polarizations configuration can completely eliminate the leakage light from the control field. Our state preparation and laser polarization lead to a single and closed ΛΛ-scheme that eliminates the detrimental absorption due to nearby states in atomic species with hyperfine separations smaller than Doppler-broadened line widths, a case where the conventional EIT configuration fails completely.