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In this paper, the potential has been investigated of using the silver(I) 3,5-diphenyltriazolate MOF—AgTz-1 as an adsorbent towards the adsorption of p-nitrophenol (PNP) from water. Based on experimental results, the best adsorption performance can be achieved at room temperature (or slightly elevated temperature) in neutral solution with the adsorption capacity Qmax being 184.8 mg/g (308 K) and 143.5 mg/g (298 K). The adsorption of PNP onto AgTz-1 is pH-dependent: at pH > 8 it can be described by the “one in, one out” anion exchange mechanism; while at pH 7 or less, some neutral 4-nitrophenol molecules may enter the interior of MOF along with 4-nitrophenolate anions via hydrogen-bonding and/or π-π stacking, accompanied by the expansion of MOF structure at higher equilibrium concentrations of PNP at 298 K and 308 K. Moreover, the adsorption efficiency of AgTz-1 remained almost the same after five consecutive cycles of adsorption–desorption.