In this paper, the pre-earthquake characteristics of b values for the intermediate magnitude earthquakes in the Tianshan seismic region of Xinjiang are studied. It was found that since 1971, the phenomena of seismic deficiency had occurred very often in the b values of the earthquakes (M>5.5) for some years before earthquakes. The interval of seismic deficincy was in good agreement with the magnitudes of happening earthquakes In the same way, the abnormal low b values would often exist in the intermediate earthquake (M>4.8), the abnormal time and the proelnet(β) of abnormal amplitude related to magnitude and we can make use of their relationships to assess the magnitude for future earthquakes. It was also found that the b values of the aftershock sequences of intermediate magnitude earthquake and of small earthquake swarms were in a low state before some time of the next one in this region and it was so even before several years of strong earthquakes. From all mentioned above, we came to the conclusion:the b value has a direct sense in physics, and the low b values, which are the reflection of fluctuating stress state, are a signal for possible occurring of strong earthquakes.