The magnetic phase diagram of Ni1-xZnxCr2O4 demonstrates complex magnetic transitions for x=0.05 with two long-range magnetic-order transitions at TC1=41K and TC2=17K. A glasslike feature emerges between TC1 and TC2 with the application of a direct current (dc) magnetic field in alternating current (ac) susceptibility measurements. Dielectric measurements show a change from the conventional dielectric to a quantum-paraelectric-like behavior without anomalies near the magnetic ordering temperature in the range 0.05<x≤1. The strong correlation among magnetic, dielectric, and ferroelectric properties near the structural relaxation temperatures 41 and 17 K confirms the emergence of multiferroic behavior in Ni0.95Zn0.05Cr2O4. A significant x-ray magnetic circular dichroism signal at the Ni site and ac susceptibility measurements indicate a spin-canting behavior between TC1 and TC2. The dilute doping of the non-Jahn-Teller Zn ion in the Jahn-Teller Ni site modulate the different magnetic exchange interactions of Ni and Cr, which could invoke spin-canting and multiferroic behaviors.