Abstract: Since the pioneering proposal by Anderson that the superconducting state of high-Tc cuprates can be described by the resonanting-valence-bond (RVB) state, a number of important results to support the idea were obtained by using the variational approach to study the t-J model. However, two major issues were not addressed at the underdoped region. The presence of "Fermi arc" in the pseudogap state and the seemingly ubiquitous stripe states have attracted many works to search for competing mechanisms not included in the theory. We will demonstrate that the fluctuation of the mean-field order parameters used in the RVB state is actually the origin of the "competition". A simple model is proposed to explain the observation of half-doped stripes observed by neutron scattering experiments on cuprates. Furthermore, we will present a numerical formalism to carry out the variational Monte Carlo calculation using the RVB state with particle number fluctuation. Up to now almost all of the numerical results were obtained using the projected wave function with a fixed number of particles or in the canonical scheme as contrary to the BCS wave function with a constant phase. Results of the two methods will be compared in this talk. Prospect of using this wave function to understand the pseudogap state will be discussed.