In this paper, robust adaptive control of a class of strict-feedback nonlinear systems with unknown control directions is investigated. A novel Nussbaum-type function is developed and a key theorem is drawn which involves quantifying the addition of multiple Nussbaum functions with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of system output are proved. A simulation example is given to illustrate the effectiveness of the proposed control scheme. (C) 2018 Elsevier Ltd. All rights reserved.