Let S 0 be the class of normalized univalent harmonic map- pings in the unit disk. A subclass V H (k) of S 0 , whose analytic part is function with bounded boundary rotation, is introduced. Some bounds for functionals, specially harmonic pre-Schwarzian derivative, described in V H (k) are given. where h and g are analytic in , with g(z0) = 0 for some prescribed point z0 ∈ . We call h and g analytic and co-analytic parts of f, respectively. If f is (locally) injective, then f is called (locally) univalent. The Jacobian and second complex dilatation of f are given by Jf(z) = |fz| 2 −|f¯| 2 = |h ' (z)| 2 −|g ' (z)| 2 and !(z) = g ' (z)/h ' (z) (z ∈ ), respectively. A result of Lewy (18) states that f is locally univalent if and only if its Jacobian is never zero, and is sense-preserving if the Jacobian is positive. The sense-preserving case implies |!(z)| < 1 in D. Throughout this paper we will assume that f is locally univalent, sense- preserving, and = D ⊂ C, with z0 = 0, where D is the open unit disk on the complex plane. Following Clunie and Sheil-Small notation (6), the class of all sense-preserving univalent harmonic mappings of D with h(0) = g(0) = h ' (0)−1 = 0 we denote SH, and its subclass for which g ' (0) = 0 by S 0 H. Several fundamental information about harmonic mappings in the plane can be found in e.g. (8). We note that each f satisfying (1.1) in D is uniquely determined by