This　article　proposes　a　novel　inverse　kinematic　approach　with　translation　transformation　matrix　based　on　screw　theory　to　solve　the　inverse　kinematic　problem　for　6R　robot　manipulator　with　offset　joint.　The　translation　transformation　matrix　is　introduced　to　convert　the　6R　robot　manipulator　with　offset　joint　to　a　new　configuration　with　intersecting　axes,　and　the　mapping　relationship　from　the　end　effector　to　the　joint　angle　is　established　along　with　the　Paden–Kahan　subproblems.　The　eight　closed　solutions　of　the　specific　configuration　are　deduced,　which　automatically　eliminate　the　singularity　solutions.　Moreover,　the　precision　and　efficiency　of　the　proposed　method　are　verified　through　a　numerical　example.　Unlike　other　approaches,　the　presented　algorithm　not　only　inherits　the　superior　accuracy　of　the　other　geometric　approaches　but　also　exhibits　an　outperform　efficiency.　Finally,　the　method　is　generalized　to　other　6R　robots,　which　has　closed-form　solutions　to　further　verify　its　versatility.　The　presented　study　provides　some　basis　for　further　investigations,　such　as　trajectory　planning　and　motion　control,　which　provides　a　new　tool　on　the　analysis　and　application　of　this　kind　of　robot　manipulator.　©　The　Author(s)　2020.