Experimental and analytical investigations are conducted on flow instability in a vertically installed liquid nitrogen shell & tube type heat exchanger. The experiments are carried out by making use of water steam as a secondary fluid and it is observed that flow instability occurs in the range of small inlet flow rate. Mode analysis of the flow instability oscillation reveals that there exists a fundamental mode and its higher harmonics up to the fourth. As the period of the fundamental mode is nearly equal to the transit time for a fluid particle to travel through the heated tube, it is suggested that this flow instability is of the density wave type. It is shown that the amount of exchanged heat, as well as the pressure drop, decrease when unstable flow oscillation occurs. An analysis of the static heat transfer and pressure drop characteristics can simulate the experimental results in the stable region. Linear stability analysis is also carried out to yield the stability map as well as the period of flow oscillation, which proved to agree with the experimental data qualitatively.