This study experimentally investigates the characteristics of Lamb wave propagating in a composite plate of varied thickness. In practical aerospace structures, there are so many parts that have varied thickness. Therefore, in order to employ the Lamb wave in a structural health monitoring of those parts, it is necessary to understand correctly the characteristics of Lamb wave for the structure with thickness variation. Thin surface-bonded piezoelectric transducers, which have great potential in integrated monitoring systems for structural health, were used to generate and receive Lamb waves. The predicted propagation velocity under the assumptions of ideal mode conversions was compared with the experimentally measured one. The validity of the results was supported by the frequency analysis of the signals. Consequently, the results show that the transient region is occurred when Lamb waves propagate across the region that thickness variation over some gradient exists.