Let K be a field and let m_0,...,m_{n} be an almost arithmetic sequence of
positive integers. Let C be a toric variety in the affine (n+1)-space, defined
parametrically by x_0=t^{m_0},...,x_{n}=t^{m_{n}}. In this paper we produce a
minimal Gr\"obner basis for the toric ideal which is the defining ideal of C
and give sufficient and necessary conditions for this basis to be the reduced
Gr\"obner basis of C, correcting a previous work of \cite{Sen} and giving a
much simpler proof than that of \cite{Ayy}.