The high-spin structure of the Ag105 nucleus has been studied by using the Mo100(B10, 5n)Ag105 reaction to search for chiral doublet bands based on the three-quasiparticle πg9/2ν(h11/2)2 configuration. The level scheme of Ag105 has been extended. New bands were found and the placement of the yrast πg9/2ν(h11/2)2 band was corrected. No side band to the yrast πg9/2ν(h11/2)2 band could be found in the present experiment. This observation indicates that the γ-soft shape in the Ag106 changed to a more γ-rigid axially symmetric shape in the yrast Ag105 configuration. However, a new pair of bands was observed to show the expected properties of a chiral doublet structure.