The advert from the Northamptonshire Police & Crime Commissioner (PCC) called for someone who was "resolutely client-centred and victim-focused".
The campaign group said PCCs were "serial offenders" in using "jargon".
Adam Simmonds, PCC, said: "The best communicators talk to people using the type of language they understand."
The existing chief constable, Adrian Lee, will be leaving the force in July.
The candidate information pack said the force was looking for an "agent of change" who can get "client-side" and "is a pioneer in blue-light collaboration".
Steve Jenner, spokesman for the Plain English Campaign, said: "The sentence that 'our chief constable must be able to see beyond the horizons of convention to make the paradigm shift' is a prime example of 'ploddledegook'.
"Police and crime commissioners seem to be repeat offenders in this regard for their mangling of the English language and this advert is borderline criminal.
"Senior police officers are probably used to this kind of jargon so they will understand it but the danger is they use it when they talk to the public."
The information pack also said the chief constable should not just issue "management speak from above" because "inevitably such statements of corporate aspiration can feel like yet another list of jargon and management-speak".
In response to the criticism, Mr Simmonds said: "Anyone who knows me knows I am a straight talker, but it is a fact, highlighted by the Plain English Society, that senior police officers have to understand the type of language used in the advert.
"What I want from our next chief constable [is] someone who can talk to politicians and judges as easily as they can their own staff and members of the public."
The deadline for applications is 1 June and the job's salary will be up to Â£150,000.
A 26-page job advert for a chief constable has been described as "ploddledegook" by the Plain English Campaign.