Zero correlation zone (ZCZ) sequences and Golay sequences are two kinds of sequences with different preferable correlation properties. It was shown by Gong \textit{et al.} and Chen \textit{et al.} that some Golay sequences also possess a large ZCZ and are good candidates for pilots in OFDM systems. Known Golay sequences with ZCZ reported in the literature have a limitation in the length which is the form of a power of 2. One objective of this paper is to propose a construction of Golay complementary pairs (GCPs) with new lengths whose periodic autocorrelation of each of the Golay sequences and periodic corss-correlation of the pair displays a zero correlation zone (ZCZ) around the in-phase position. Specifically, the proposed GCPs have length $4N$ (where, $N$ is the length of a GCP) and ZCZ width $N+1$. Another objective of this paper is to extend the construction to two-dimensional Golay complementary array pairs (GCAPs). Interestingly the periodic corss-correlation of the proposed GACPs also have large ZCZs around the in-phase position.