In order to obtain tunable, very narrow linewidth laser radiation of high power and energy, we have developed a self-injected tunable dye laser based on a new technique. In this paper the theory of mode coupling in dye lasers is used to study the relationship between tunable bandwidth range and injected power. It is shown that the tuning range of a self-injected dye laser is associated with the injected power p and the state function of the amplifying cavity; when the switching time of the cavity switch (Pockel cell) is fixed, the tuning range increases almost linearly as the injected power increases. The experimental results agree with the theoretical analysis, which is useful for actual injection laser devices.