Variability is one of the main observational characteristics of blazars. Studying variability is an efficient method to reveal the nature of active galactic nuclei. In the present work, we report optical R-band photometry observations of a TeV blazar, 1ES 2344 + 514, carried out with a 70 cm telescope in the period of 1998 July–2017 November at Abastumani Observatory, Georgia. Based on the optical R-band observations, the optical variation behaviors on both short timescales and long timescales are investigated. Three methods (Jurkevich, discrete correlation function, and power spectrum analysis) are used to investigate periodicity in the light curve. In addition, combined with multiwavelength data, the jet physical properties are discussed. The following conclusions are drawn: (1) A variability of ΔR = 0.155 mag (15.356 − 15.201 mag) over a timescale of ΔT = 12.99 minutes is detected during our 628 days of monitoring. (2) According to the Kelvin–Helmholtz thermal instability, if the magnetic field intensity (B) for the source is greater than a critical value (B
c
), it will reduce the incidence of intraday variations in the light curves. (3) The physical parameters of the dissipation region are obtained by fitting the spectral energy distribution with a one-zone synchrotron self-Compton model for the average and flare states. (4) The three methods show that there are periods of P = 2.72 ± 0.47 yr, P = 1.61 ± 0.18 yr, P = 1.31 ± 0.17 yr, and P = 1.05 ± 0.07 yr. When a binary black hole system is adopted with a period of P = 2.72 ± 0.41 yr, we obtain the orbital parameters for the binary black hole system as follows: M = 8.08 × 109
M
⊙, the sum of the semiaxes is r = 7.18 × 1016 cm, and the lifetime of the binary black hole is τ
merge = 6.24 × 102 yr.