The thieves have targeted houses in Staple Hill, Kingswood and Warmley during the last four weeks.
In one incident this week, a three-seater swing complete with canopy was taken from a garden.
Police said all the thefts happened at night and, because of the size of the items taken, must have involved a vehicle to take them away.
Officers want to hear from anyone who has any information about the thefts or who has been offered any garden furniture under suspicious circumstances.
Homeowners are also reminded to ensure side gates are locked and are being asked to consider the installation of security lights to safeguard their properties.
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