The purpose of this paper is to investigate the mechanical properties and the lime-based binder hardening of green concretes made of rice husk or hemp hurd. Concrete specimens were subjected to different curing conditions. Under natural carbonation, specimens were cured during 10 months either in a climate-controlled room (20 degrees C - 50%RH) or exposed outdoors. The work also focused on an accelerated carbonation curing (CO2 curing) aiming to improve the short term compressive strength (1-2 months) of the concrete materials. Compressive strength tests were conducted at different dates until 10 months of natural carbonation and after CO2 curing. Powdered matrix samples were collected in the bulk and on the surface of the specimens to investigate carbonation and hydration of the binder by thermal analysis and a phenolphthalein test was used to provide information about the carbonation depth. Under natural carbonation, the results indicated that the lime-based binder was almost hardened in the same way for both concretes with a similar rate of carbonation. However, the rice husk concrete was characterized by a ceiling effect of mechanical performances overtime, which was attributed to the lower bonding strength between rice husks and lime. Concerning specimens exposed outdoors, the strength gain over time was more significant owing to more favorable humidity conditions for carbonation. The accelerated carbonation curing led to an increase of mechanical properties of the concretes in the short term. The compressive strength after CO2 curing was approximately equivalent to those obtained after 10 months of outdoor exposure under natural carbonation.