A turn-back coaxial gas pressurizing pump, comprising: a primary cylinder, a primary piston provided in the primary cylinder, a secondary cylinder serving as a rod of the primary piston, a pressure bar fixed to the secondary cylinder, and an air pump bonnet covering an open end of the primary cylinder; wherein a secondary piston and a piston rod are provided in the secondary cylinder, wherein the primary cylinder, the secondary cylinder, and the piston rod are arranged coaxially, a rear end of the piston rod extends through the primary piston and is fixed on a bottom of the primary cylinder, a first non-returning adaptive valve is placed between the piston rod and the primary piston, a primary compression chamber formed by a front end of the primary piston is provided in the primary cylinder and is configured to communicate with an external air via a non-returning intake valve, wherein a secondary compression chamber formed by a front end of the secondary piston is provided in the secondary cylinder and is configured to communicate with a pressure output gas line via a non-returning output valve, wherein the primary compression chamber communicates with a transition chamber formed by a rear end of the secondary piston which is provided in the secondary cylinder via the first non-returning adaptive valve in a one-way manner, and wherein the transition chamber communicates with the secondary compression chamber via a second non-returning control valve in a one-way manner, characterized in that, a first annular notch is fluted on a contact of a front face of the primary piston with an internal face of the primary cylinder, and a first seal assembly is fitted into the first annular notch; a second annular notch is fluted on a contact of a front face of the secondary piston with an internal face of the secondary cylinder, and a second seal assembly is fitted into the second annular notch; the seal assemblies consist of an elastic seal ring and a wear-resistant ring gasket, the ring gasket has a recessed annular groove, and the elastic seal ring is placed between the annular groove and a front annular opening of the pistons. a primary cylinder, a primary piston provided in the primary cylinder, a secondary cylinder serving as a rod of the primary piston, a pressure bar fixed to the secondary cylinder, and an air pump bonnet covering an open end of the primary cylinder; wherein a secondary piston and a piston rod are provided in the secondary cylinder, wherein the primary cylinder, the secondary cylinder, and the piston rod are arranged coaxially, a rear end of the piston rod extends through the primary piston and is fixed on a bottom of the primary cylinder, a first non-returning adaptive valve is placed between the piston rod and the primary piston, a primary compression chamber formed by a front end of the primary piston is provided in the primary cylinder and is configured to communicate with an external air via a non-returning intake valve, wherein a secondary compression chamber formed by a front end of the secondary piston is provided in the secondary cylinder and is configured to communicate with a pressure output gas line via a non-returning output valve, wherein the primary compression chamber communicates with a transition chamber formed by a rear end of the secondary piston which is provided in the secondary cylinder via the first non-returning adaptive valve in a one-way manner, and wherein the transition chamber communicates with the secondary compression chamber via a second non-returning control valve in a one-way manner, characterized in that, a first annular notch is fluted on a contact of a front face of the primary piston with an internal face of the primary cylinder, and a first seal assembly is fitted into the first annular notch; a second annular notch is fluted on a contact of a front face of the secondary piston with an internal face of the secondary cylinder, and a second seal assembly is fitted into the second annular notch; the seal assemblies consist of an elastic seal ring and a wear-resistant ring gasket, the ring gasket has a recessed annular groove, and the elastic seal ring is placed between the annular groove and a front annular opening of the pistons.