Abstract: The research on hypersonic boundary layer transition is a recent focal point in aerodynamics. For the so-called 'natural transition', where the level of environment disturbance is low, stability analysis has been proved to be a helpful technique in studying evolution of disturbances. On the other hand, temperatures in hypersonic boundary layer increase dramatically with Mach number. Extremely high-temperature causes the so-called 'real-gas effects', or more exactly, 'thermal-chemical non-equilibrium effects', which invalidates the calorically perfect gas assumption, and inevitably influences the stability and transition process. The flow treated in this paper is a hypersonic boundary layer on a flat-plate with thermal-chemical non-equilibrium effects. Linear stability theory (LST) is applied to study the effects thermal-chemical process take on modal instability. Meanwhile, the evolution and synchronization process between discrete and continuous spectrum are explored. Results for the 2-D hypersonic boundary layer where the 2nd mode dominates are concluded as follows. Firstly, disturbances are more thermal-chemical frozen than the basic flow. Secondly, the new term in the disturbance equation introduced by the non-equilibrium source term has little effects on stability. The differences in stability behaviors between non-equilibrium and calorically perfect gas mainly attribute to different basic flow profiles. Thirdly, speed of sound is crucial to Mack modes. The different evaluation of the speed of sound for thermal-chemical equilibrium flow is the answer to the unconventional trend that a cooler and thinner boundary layer has lower 2nd-mode frequency.