A Shape Memory Alloy (SMA) enabled Overtopping Wave Energy Converter (OWEC) that maximizes its overtopping discharge, and thus energy output under different wave conditions is presented. Among all the parameters affecting the overtopping discharge rate, the crest freeboard height is the most influential one to control the overtopping discharge rate and the stored overtopping volume behind it. Currently, all the OWEC crest freeboard heights are fixed by design to maximize the discharge rate on one particular sea state. In the present study, we show that the SMA can adjust the crest freeboard height through a control system based on the sea state and achieve an optimal overtopping discharge rate. A scaled OWEC model is built in the lab with its crest freeboard height controlled by springs made of SMA. The length (and thus tension) of the springs is controlled by temperature changes by changing the passing current through the springs. By adjusting the length of the springs based on the incoming wave condition, we adjust the freeboard to an optimal height known to generate a maximum overtopping discharge rate for energy conversion. This smart material-enabled design can maximize the overtopping discharge and thus the output power of the OWEC under various wave conditions. Furthermore, the simplicity of using SMA springs as the actuator leads to the minimum number of moving mechanical parts, which can remarkably decrease maintenance costs. As the proof of concept, two types of tests are conducted in the laboratory using the same OWEC model under several random wave trains generated from spectra with different significant wave heights - one type with a fixed crest freeboard height and the other type featuring the adjustable crest freeboard height controlled by the springs. The substantial increase of harvested output power in the OWEC with the adjustable crest freeboard height may pave the way for more efficient wave energy conversion systems.