This paper analyzes the ergodic capacity of a user-centric virtual cell (VC) dense network, where multiple access points (APs) form a VC for each user equipment (UE) and transmit data cooperatively over millimeter wave (mmWave) channels. Different from traditional microwave radio communications, blockage phenomena have an important effect on mmWave transmissions. Accordingly, we adopt a distance-dependent line-of-sight (LOS) probability function and model the locations of the LOS and non-line-of-sight (NLOS) APs as two independent non-homogeneous Poisson point processes (PPP). Invoking this model in a VC dense network, new expressions are derived for the downlink ergodic capacity, accounting for: blockage, small-scale fading and AP cooperation. In particular, we compare the ergodic capacity for different types of fading distributions, including Rayleigh and Nakagami. Numerical results validate our analytical expressions and show that AP cooperation can provide notable capacity gain, especially in low-AP-density regions.