Is zener diode a linear device?

Zener diode is not a linear device... it is non-linear one.

Since linear devices are those devices which have linear characteristics(V-I CHAR.), or follows the Ohm's law i.e. voltage is directly proportional to current.

but in case of Zener diode ohm's law fails down. the V-I char. in both forward biased & reverse biased condition is non-linear. So. Zener diode is non-linear device