This paper deals with the local scour around a pipeline exposed to combined waves and current in the shallow water zone. To investigate the characteristics of the scour around a pipeline on the sea bed, experiments were performed according to the various pipe diameters, wave periods, wave heights, and current velocities. Wave generator and current generator were used for the experiments. Two current directions were used ; co-direction and counter direction to the waves. With the experimental results, the correlations between the scour depths and non-dimensional parameters such as Keulegan-Carpenter number(KC), Froude number(Fr), Ursell number(Ur) and velocity ratio were analysed. The relative scour depths were found obviously to be dominated by the wave component when the velocity ratio function approaches zero and those are gorverned by the current component when the velocity ratio approaches unity. Velocity ratio function was approved to be a proper parameter which is able to express the change of the scour in the combined wave and current zone. Also considering the orbital velocity and the current velocity into Fr numer and KC number respectively, scour depths show more favorable correlationship with the parameters.