The nature of magnetism in the doubly-diluted spinel ZnTiCoO4 is reported here employing the temperature and magnetic field dependence of dc- and ac-susceptibilities, and heat capacity (CP) measurements. The antiferromagnetic Néel temperature (TN~13.8 K) is determined from the peak in the ∂(χT)/∂T vs. T plot and the Power law yields the spin-glass freezing temperature Tg ~ 12.9 K with critical exponent zν ~ 11.75. Since the magnitudes of t
o and zν depend on the magnitude of Tg, a procedure is developed to find the optimum value of Tg = 12.9 K. A similar procedure is used to determine the optimum T0 = 10.9 K in the Vogel-Fulcher law yielding Ea/kB = 95 K, and t
0 = 1.6 ×10-13 sec. It is argued that the comparatively large magnitude of the Mydosh parameter Ω = 0.024 and Ea/(kBT0)=8.7(>>1) suggests cluster-spin-glass state in ZnTiCoO4 below Tg. In the CP vs T data from 1.9K to 50K, the observation of only a broad peak near 20K and absence of λ-type anomaly near TN or Tg combined with the reduced value of change in magnetic entropy from 50K to 1.9K suggests the presence of only short-range ordering in the system, consistent with spin-glass state. The field dependence of Tg shows slight departure from the non-mean-field Almeida-Thouless line. Strong temperature dependence of magnetic viscosity S and coercivity HC without exchange bias, both tending to zero on approach to Tg from below, further support the spin-glass state which results from magnetic dilution driven by Zn2+ and Ti4+ ions leading to magnetic frustration. Magnetic phase diagram in the H-T plane is established using the high-field magnetization data M(H,T) for T < TN which reveals rapid decrease of Tg with increase in H whereas decrease in TN with increase in H is weaker, typical of antiferromagnetic systems.