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We investigate exact traveling wave solutions of the scalar Qiao equation proposed by Li and Qiao (2010 J. Math. Phys. 51 042703) using the generalized auxiliary equation method. This equation is known to have bi-Hamiltonian structure and Lax pair, which imply integrability of the equation for a fixed value of k. Symmetries of the scalar Qiao equation and its solutions are also considered. The obtained solutions include kink and antikink solitons, bright and dark solitons, singular solutions and exponential solutions. This method could be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics. This work could be also relevant for numerical studies of the scalar Qiao equation.