A new structure of Reluctance linear-rotary magnetic gear（ RLRMG） is proposed. The poles on screw and nut are composed of semi-oblique ring type permanent magnetic and soft magnetic,and call the poles as convex tooth. The permanent magnetic and soft magnetic convex tooth are arranged alternately. The permanent convex teeth on the screw and nut are both radially magnetized and the magnetized direction is opposite.The static characteristics of RLRMG are simulated with FEM. It is proved that the RLRMG can realize smooth transmission. The concept of Pole pitch ratio（ PPR） is proposed in order to describe the relationship of pole width and pitch. The relationship between PPR and static characteristics of RLRMG,thrust density and specific thrust are investigated with simulation. Result shows that when PPR is in the interval( 0,0. 5],RLRMG can realize smooth transmission. When PPR is in the range of( 0,0. 3],the change of thrust force and thrust density of nut are all less than 7%. When PPR is 0. 3,the specific thrust has the maximum value,that is has the maximum pole utilization ratio. When design a RLRMG,PPR should be 0. 3.