This invention relates to a single cone bit with offset axis and composite cones for oil and gas drilling, mining and other subterranean drilling operations. The bit consists of a head body and a cone. The cone section has a shape of composite cones. The outer circumference of the cone is composed of from back face of the cone to top of the cone an extended gage surface, an outer cone surface and a main cone surface. A plurality of cutting elements is mounted onto each cone surface. A head journal at lower end of the head body is for rotatablely connection with the cone. Between the axis of head journal and the axis of the bit, there is an offset value d along rotating direction of the cone. A gage pad is arranged on head body at a location opposite to the offset direction of the head journal. The gage pad is fitted with inserts or hardfaced with wear resistant alloy to prevent bit from whirling and prevent head body from being worn out and to ensure gage protection. Junk slots are machined along the side of head body and jet ports are arranged at lower bevel of the head body to guarantee cuttings removal and effective cleaning results. This invention improves the bit's ability to break rocks through impact for specific use in hard formations. The bit performance is obviously improved and overall drilling cost reduced.