A two-dimensional off-lattice protein model with two species of monomers, hydrophobic and hydrophilic, was studied. Low-energy configurations in the model were optimized using the improved energy landscape paving (ELP+) method. In ELP+, the energy landscape paving (ELP) was first applied to search for the low-energy states. After the ELP led to the basins of the local energy minima, the additional degree-of-freedom of bond length was introduced, and the gradient descent method was then used to search for lower energy states near the local minima. Numerical results show that the proposed methods are quite effective for finding the ground states of proteins. A comparison between ELP+ and other methods is made.