Fault diagnosis of discrete-event systems (DESs) has received a lot of attention in industry and academia during the last two decades. In DES based diagnosis, the two main discussed topics are offline diagnosability analysis and online diagnosis. A pioneering approach that led to the development of various techniques is based on the so-called diagnose. However, this approach suffers from the combinatorial explosion problem due to the exponential complexity of construction. To partially overcome this problem, an efficient approach to construct a symbolic diagnoser is proposed in this paper. The proposed approach consists in constructing a diagnoser based on the symbolic observation graph (SOG), which combines symbolic and enumarative representations. The construction of the diagnoser as well as the verification of diagnosability are performed simultaneously on the fly, which can considerably reduce the state space of the diagnoser and thus the overall running time. To evaluate the efficiency and the scalability of the approach, some experimental results are presented and discussed based on a DES benchmark.