The production and research of ultracold heteronuclear molecules have aroused the great interest recently. On the one hand, these molecules are extremely popular in experiments for exploring the collision dynamic behaviors in threshold, photoassociative spectrum and strong dipole-dipole interactions. On the other hand, ultracold polar molecules populated at deeply bound levels in the singlet ground state are the right candidates to investigate quantum memories for quantum simulation, and to study strongly interacting quantum degenerate gases. The precise knowledge of cold collision processes between two different types of alkali atoms is necessary for understanding and utilizing ultracold heteronuclear molecules, sympathetic cooling, and thus formation of two species BEC. The goal of the present investigation is to study the collisions between ultracold sodium atoms and cesium atoms. We systematically demonstrate simultaneously trapping ultracold sodium and cesium atoms in a dual-species magneto-optical trap (MOT). The sodium atom trap loss rate coefficient Na-Cs is measured as a function of Na trapping laser intensity. At low intensities, the trap loss is dominated by ground-state hyperfine-changing collisions, while at high intensities, collisions involving excited atoms are more important. A strong interspecies collision-induced loss for Na atoms in the MOT is observed. In order to obtain the trap loss coefficient Na-Cs, we proceed in two steps. First, the Cs repumping laser is blocked to avoid the formation of ultraold Cs atoms. The loading process of Na atoms is recorded when the Cs trapping laser is on. Second, the loading curves of the Na atoms are obtained as Cs atoms are present with the repumping laser beams. The total losses PNa and PNa' are acquired by fitting the two loading curves of trapped Na atoms. Thus, the trap loss coefficient Na-Cs can be derived from the difference between total losses PNa and PNa' divided by the density of the Cs atoms. The coefficient Na-Cs decreases in a range of 5-10mW/cm2, which originates from the hyperfine-state changing (HFC) collision. A Doppler model is used to calculate the Na atom trap depth, in that the atom trap depth and exoergic energy determine the behavior of the collisional trap loss rate coefficient. The three corresponding calculated critical intensities of Na trapping laser are 7.98, 14.82, 16.2 mW/cm2 respectively in the Na-Cs HFC collision process. The first calculated critical intensity value agrees well with the experimental result. Our work provides a valuable insight into HFC collision between Na and Cs atoms and also paves the way for the production of ultracold NaCs molecules using Photoassociation (PA) technology. Furthermore, the experimental results lay a great basis for the obtainments of high sensitive heteronuclear NaCs molecular PA spectrum and the creation of deeply bound ground state molecules.