<p>Linear temporal logic (LTL) model checking faces a significant challenge known as the state-explosion problem. The on-the-fly method is a solution that constructs and checks the state space simultaneously, avoiding generating all states in advance. But it is not effective for concurrent interleaving. Unfolding based on Petri nets is a succinct structure covering all states that can mitigate this problem caused by concurrency. Many state-of-the-art methods optimally explore a complete unfolding structure using a tree-like structure. However, it is difficult to apply such a tree-like structure directly to the traditional on-the-fly method of LTL. At the same time, constructing a complete unfolding structure in advance and then checking LTL is also wasteful. Thus, the existing optimal exploration methods are not applicable to the on-the-fly unfolding. To solve these challenges, we propose an LTL model-checking method called on-the-fly unfolding with optimal exploration. This method is based on program dependence net (PDNet) proposed in the previous work. Firstly, we define conflict transitions of PDNet and an exploration tree with a novel notion of delayed transitions, which differs from the existing tree-like structure. The tree improves the on-the-fly unfolding by exploring each partial-order run only once and avoiding enumerating all possible combinations. Then, we propose an on-the-fly unfolding algorithm that simultaneously constructs the exploration tree and generates the unfolding structure while checking LTL. We implement a tool for verifying LTL properties of concurrent programs. It also improves traditional unfolding generations and performs better than <i>SPIN</i> and <i>DiVine</i> on the used benchmarks. The core contribution of this paper is that we propose an on-the-fly unfolding with an optimal exploration method for LTL. It avoids the complete enumeration of concurrent combinations from traditional unfolding generation.</p>