Single antenna vector OFDM (V-OFDM) system has been proposed and investigated in the past. It contains the conventional OFDM and the single carrier frequency domain equalizer (SC-FDE) as two special cases and is flexible to choose any number of symbols in intersymbol interference (ISI) by choosing a proper vector size. In this paper, we develop cyclic delay diversity (CDD) transmission for V-OFDM when there are multiple transmit antennas (CDD-V-OFDM). Similar to CDD-OFDM systems, CDD-V-OFDM can also collect both spatial and multipath diversities. Since V-OFDM first converts a single input single output (SISO) ISI channel to a multi-input and multi-output (MIMO) ISI channel of order/length $K$ times less, where $K$ is the vector size, for a given bandwidth, the CDD-V-OFDM can accommodate $K$ times more transmit antennas than the CDD-OFDM does to collect all the spatial and multipath diversities. This property will specially benefit a massive MIMO system. We show that with the linear MMSE equalizer at each subcarrier, the CDD-V-OFDM achieves diversity order $d_{\text{CDD-V-OFDM}}^{\text{MMSE}} = \min \{ \lfloor 2^{-R}K \rfloor, N_t L \} +1$, where $R$ is the transmission rate, $N_t$ is the number of transmit antennas, and $L$ is the ISI channel length between each transmit and receive antenna pair. Simulations are presented to illustrate our theory.