Dust grains grow in interstellar clouds by accretion and coagulation. In this paper, we focus on these two grain growth processes and numerically investigate how they interplay to increase the grain radii. We show that accretion efficiently depletes grains with radii on a time-scale of 10 Myr in solar-metallicity molecular clouds. Coagulation also occurs on a similar time-scale, but accretion is more efficient in producing a large bump in the grain size distribution. Coagulation further pushes the grains to larger sizes after a major part of the gas-phase metals are used up. Similar grain sizes are achieved by coagulation regardless of whether accretion takes place or not; in this sense, accretion and coagulation modify the grain size distribution independently. The increase of the total dust mass in a cloud is also investigated. We show that coagulation slightly ‘suppresses’ dust mass growth by accretion but that this effect is slight enough to be neglected in considering the grain mass budget in galaxies. Finally, we examine how accretion and coagulation affect the extinction curve: the ultraviolet slope and the carbon bump are enhanced by accretion, while they are flattened by coagulation.