We study the features of electromagnetically induced transparency (EIT) in a single Λ-type three-level atom placed in a high-finesse cavity under the action of a coupling laser and a probe laser. Our calculations show that three transparency windows appear when the pump strength is large enough. This can be explained by the residual pump in the cavity mostly resulting in energy splitting. The level |3〉 is split into four slightly different energy levels, and interference takes place between the excitation pathways. Furthermore, it is also shown that the frequencies of the EIT windows can be tuned by changing the coupling field detuning Δ2, and that the reflection profile is very sensitive to the cavity field detuning Δc.