The multi-input multi-output (MIMO) technology plays an important role in link transmissions. This article considers the general case for the ergodic capacity in doubly correlated frequency-selective MIMO channel. In the study, the geometrical MIMO channel model is presented. Based on the formula of MIMO ergodic capacity, the capacity limits are studied with arbitrary finite number of antennas in the frequency-selective MIMO channel. It first derives the exact expressions for the upper bound and lower bound in doubly correlated MIMO channel. The results for the single-ended correlation and independent identically distributed (i.i.d.) MIMO channel are also obtained as special cases. Then the simple expressions of the capacity bounds are attained at high SNR. Finally, results are provided by Monte Carlo simulations to verify the tightness of the derived bounds. The multi-input multi-output (MIMO) technology plays an important role in link transmissions. This article considers the general case for the ergodic capacity in doubly correlated frequency-selective MIMO channel. In the study, the geometrical MIMO channel model is presented. Based on the formula of MIMO ergodic capacity, the capacity limits are studied with arbitrary finite number of antennas in the frequency-selective MIMO channel. It first derives the exact expressions for the upper bound and lower bound in doubly correlated MIMO channel. The results for The single-ended correlation and independent identically distributed (iid) MIMO channel are also obtained as special cases. Then the simple expressions of the capacity bounds are attained at high SNR. Finally, results are provided by Monte Carlo simulations to verify the tightness of the derived bounds.