When applied to practical applications, existing chaotic systems exhibit many weaknesses, including discontinuous chaotic intervals and easily predicted chaotic signals. This study proposes an n-dimensional chaotic model (nD-CM) to resolve the weaknesses of existing chaotic systems. nD-CM can produce chaotic maps with any desired dimension utilizing existing 1D chaotic maps as seed chaotic maps. To demonstrate the effect of nD-CM, we generate three 2D and one 3D chaotic map as examples, utilizing three 1D chaotic maps as the seed maps. The evaluation and experiment results show that these newly generated chaotic maps can obtain continuous and wider chaotic intervals and better performance using the indicators of the Lyapunov exponent, sample entropy and correlation dimension, compared to existing maps. To further show the practicality of nD-CM, the generated maps are additionally applied to secure communication. The experimental results show that these chaotic maps exhibit much better performance in resisting transmission noise in this application than existing chaotic maps.