We develop a new, lattice effects-free lattice Boltzmann model for simulating crystal growth from supersaturated solution. Simulations of crystal growth from a single or multiple nuclei in a domain initially filled with supersaturated solution are presented, such as in the case of gas hydrate formation. We find that as the process changes from diffusion-controlled to surface reaction-controlled, the crystal transforms from open cluster-type structure, via compact coral-type structure, to compact circular structure, and correspondingly, the fractal dimension of the crystal structure increases from a value close to that of a diffusion-limited aggregation (DLA) structure to the Euclidian value for a circle. At a high Damkohler number, crystal formed from a single nucleus becomes more compact as the saturation increases. At a low Damkohler number, the crystal has a fairly round shape for different saturation values and the effect of saturation is insignificant.