In this paper, we propose an infinite class of Boolean functions with four-valued Walsh spectra. These functions have a simple trace expression of the form f(x) = trn 1 (??d(2 n +1)) + tr2n 1(bx) for b ?? F2 2n and d satisfying d(2l +1) = 2i(mod 2n-1) with integers I and i, where x ?? F2 2n. Their cryptographic properties, including balancedness, spectrum distribution, nonlinearity, algebraic degree and algebraic immunity, are investigated. We prove that the proposed functions have high nonlinearity, and algebraic degrees n - gcd(n, I) + 2. Our computer simulation shows these functions have optimal or suboptimal algebraic immunity.