This paper considers the quantized output feedback control design for a class of ncertain nonlinear systems. Different from the existing literature, the  onlinear growth of the ystems under investigation depends on the unmeasured states, which makes the observer design inthe existing literature inapplicable, and renders the performance analysis for the closed-loop ystem more complex and difficult. First, a new high-gain observer is introduced to reconstruct he unmeasured states. Then, by applying the set-valued maps and recursive control design ethod in the existing literature, a quantized output feedback controller is designed. Finally, y the cyclic-small-gain theorem and dynamic quantization strategy, a sufficient condition is iven to guarantee that all states of the closed-loop system are bounded and that output can  beultimately arbitrarily small.