Summary: We introduce a self-similar Gaussian process called the generalized sub-fractional Brownian motion. This process generalizes the well-known sub-fractional Brownian motion introduced by \textit{T. Bojdecki} et al. [Stat. Probab. Lett. 69, No. 4, 405--419 (2004; Zbl 1076.60027)]. We prove the existence and the joint continuity of the local time of our process. We use the concept of local nondeterminism for Gaussian process introduced by \textit{S. M. Berman} [Indiana Univ. Math. J. 23, 69--94 (1973; Zbl 0264.60024)] and the analytic method used by \textit{S. M. Berman} [Trans. Am. Math. Soc. 137, 277--299 (1969; Zbl 0184.40801)] for the calculation of the moments of local time.