We report on charge state measurements of laser-accelerated carbon ions in the energy range of several MeV penetrating a dense partially ionized plasma. The plasma was generated by irradiation of a foam target with laser-induced hohlraum radiation in the soft x-ray regime. We use the tricellulose acetate (C_{9}H_{16}O_{8}) foam of 2 mg/cm^{3} density and 1 mm interaction length as target material. This kind of plasma is advantageous for high-precision measurements, due to good uniformity and long lifetime compared to the ion pulse length and the interaction duration. We diagnose the plasma parameters to be T_{e}=17 eV and n_{e}=4×10^{20} cm^{-3}. We observe the average charge states passing through the plasma to be higher than those predicted by the commonly used semiempirical formula. Through solving the rate equations, we attribute the enhancement to the target density effects, which will increase the ionization rates on one hand and reduce the electron capture rates on the other hand. The underlying physics is actually the balancing of the lifetime of excited states versus the collisional frequency. In previous measurement with partially ionized plasma from gas discharge and z pinch to laser direct irradiation, no target density effects were ever demonstrated. For the first time, we are able to experimentally prove that target density effects start to play a significant role in plasma near the critical density of Nd-glass laser radiation. The finding is important for heavy ion beam driven high-energy-density physics and fast ignitions. The method provides a new approach to precisely address the beam-plasma interaction issues with high-intensity short-pulse lasers in dense plasma regimes.