We report an experimental observation of the variation in linewidth of the electromagnetically induced transparency (EIT) resonance in a three-level Λ-type system for several laser bandwidths in a Rb vapor cell, with and without a buffer gas. It is found, using narrow bandwidth (about 20 kHz) diode laser for both coupling and probe beams, that the linewidth of the EIT resonance can be significantly narrowed in the Rb vapor cell with the buffer gas. The results are in good qualitative agreement with a simple theoretical calculation.