When ultrashort pulse laser interacts with near-critical-density plasma, extremely strong transient electromagnetic field will generate a great variety of nonlinear phenomena, such as efficient pulse absorption, magnetic self-channeling, nonlinear coherent structure, and electron and ion acceleration. It is of great significance to make a profound study of these physical processes for studying the laser-plasma interaction. Here in this work, we investigate the near-critical-density plasma structure and its temporal evolution by using proton radiography. The plasma is generated by the interaction of ultra-intense femtosecond laser (I \sim 3.6 × 10¹⁸ W/cm²) with high-density gas-jet target, which can produce plasma with electron density n_e \sim 0.7n_c (here, n_c is the near-critical-density) for 800 nm laser. The proton beam is produced by the interaction of another ultra-intense femtosecond laser with stainless steel foil target. In the experiment, the proton beam is split into two asymmetric spots. On the one hand, the distance between two spots first increases rapidly and decreases slowly as time goes by. On the other hand, the size of proton beam spot on the right side is obviously lager than the one on the left side. The modification of proton beam profile indicates that a transient electric field with a maximum amplitude of 10⁹ V/m is produced when ultrashort laser pulse interacts with the plasma. Besides, the electric field in the direction of laser propagation axis is stronger than that in the opposite direction. When the proton beam goes through the laser-plasma interaction area, most of the protons enter into the electric field in the direction of laser propagation axis, only a small number of protons enter into the electric field in the opposite direction, resulting in the fact that the proton beam is split into two asymmetric spots. The space-charge field in the plasma is induced by the laser ponderomotive force which expels the electrons piled up into a step-like profile. This field can be sustained for a long time, as the ions expand slowly because of the coulomb repulsion between ions, and the hot electrons continue to move forward with energy of a few MeV. At the end, these expanded ions gradually recombine with the reflowed electrons, causing the space-charge field to weaken until it disappears eventually. As a result, the deflection of the proton beam by the electric field in the plasma is also weakened, so the distance between proton beam splitting spots is correspondingly reduced. The hypothesis is justified by the particle-in-cell simulations. The results may have important implications in laser wake-field electron acceleration, ion acceleration and fast ignition scheme to inertial confinement fusion.