<p>In this paper, we propose two new Halpern relaxed projection methods for solving the partially pseudomonotone and Lipschitz continuous variational inequality problems in a real Hilbert space. First, by basing on strongly quasi-nonexpansiveness of the relaxed solution mappings and Halpern technique, we present a strong convergence algorithm. Next, by using the strong convergence and Tseng’s linesearch techniques, we give the second algorithm which avoids the need to know the Lipschitz constant of the cost mapping. Finally, primary numerical experiments compare with some algorithms using projections and illustrate the behaviors of the proposed algorithms.</p>