This paper examines the sizing problem of an energy storage system (ESS) for a direct wave energy converter as the SEAREV. The aim of this ESS is to insure a smoothed output power profile. First, the output set point power is considered constant and equal to the average produced power during a sea state representative time (about two hours). Two others causal method of smoothing will be studied in a second part. We introduce two state of charge (SOC) control strategies in order to maintain SOC between two limits and also two power quality criteria in order to quantify the difference of the real output grid power with respect to the desired set point. The life cycle economical cost of the ESS is analyzed according to its storage energy rating in case of supercapacitor technology. The life expectancy is also studied in order to determine a possible replacement of the ESS during its life.