A room temperature fast-curing organopolysiloxane composition which has excellent fast curability as well as deep curability is provided without using an organic compound having C═O group and the organic compound having NH2 group which are the volatile components. A method for curing such composition is also provided. The room temperature fast-curing organopolysiloxane composition comprises: (A) 100 parts by weight of a diorganopolysiloxane having both ends terminated with hydroxy group and/or a hydrolyzable group; (B) 0.5 to 10 parts by weight of a silane and/or a siloxane having at least 3 alkenoxysilyl groups in its molecule and being capable of forming a compound having —NH2 group by hydrolysis; (C) 0.5 to 10 parts by weight of a silane and/or a siloxane having at least 3 aminosilyl groups in its molecule and being capable of forming a compound having —NH2 group by hydrolysis; and (D) 0.01 to 10 parts by weight of a curing catalyst.