The council is spending more than £20,000 on the barriers at Graves park petting farm to protect the animals.
It says a lamb was stolen on another occasion and the farm shop has also been broken into.
Horrified workers said the goats had been "randomly killed" overnight on October 19.
Graves Park was already being revamped with a new toilet block, animal field shelters, improvements to Rose Garden play area and Cobnar Road play area and better paths but the council has now budgeted extra money for the barriers.
In a report, officers say: “Following the killing of four goats, officers have had to review the options for improving security at the farm.
Strictly Come Dancing and Springwatch presenters support project to save endangered Turtle DovesSurge in popularity of farm shops 'vital' to sustaining agricultural sector“The perimeter of the main farm area and surrounding paddocks has a combination of low level stock fencing, beech hedging and a wall as its perimeter.
“Most of the fencing and the gates within it are low level and a particular vulnerability is the gate leading to the rear of the farm which is a simple five bar gate.
“Previous break-ins to the farm area have resulted in a lamb being stolen and damage to, and loss of merchandise from the farm shop.
“There is now an urgent need to upgrade the perimeter to ensure 8ft high barriers surround the entire site by replacing low level stock fencing and gates to all sides.”
The council is also investing almost £262,000 in improving staff welfare facilities at the farm, which officers say are dilapidated.
Water from the drains has damaged a cabin and there’s no heating and hot water. A building housing the animal isolation unit is also in poor condition and needs replacing.
The report adds: “Due to the very poor condition of the facilities they are uneconomical to repair. If the facilities are not updated they will fail, meaning that the animal farm will close to the public. We will demolish or remove existing dilapidated units and replace with new.”