Model checking is a powerful and widespread technique for the verification of finite distributed systems. However, the main hindrance for wider application of this technique is the well-known state explosion problem. During the last two decades, numerous techniques have been proposed to cope with the state explosion problem in order to get a manageable state space. Among them, on-the-fly model-checking allows for generating only the ”interesting” part of the model while symbolic model-checking aims at checking the property on a compact representation of the system by using Binary Decision Diagram (BDD) techniques. In this paper, we propose a technique which combines these two approaches to check LTL∖X state-based properties over finite systems. During the model checking process, only an abstraction of the state space of the system, namely the symbolic observation graph, is (possibly partially) explored. The building of such an abstraction is guided by the property to be checked and is equivalent to the original state space graph of the system w.r.t. LTL∖X logic (i.e. the abstraction satisfies a given formula ϕ iff the system satisfies ϕ). Our technique was implemented for systems modeled by Petri nets and compared to an explicit model-checker as well as to a symbolic one (NuSMV) and the obtained results are very competitive.