The move is part of the global packaging group's European restructure, which is in response to "relocation of parts of our customer base to low-cost, high-growth markets such as Eastern Europe", according to the firm.
It also quoted competitive markets, lower retail prices, overcapacity, as well as increases in raw material, energy and transport costs as factors in the decision to close the plant.
"We have examined in detail a number of possible alternatives, but we believe no viable solution exists to the financial and strategic problems facing these businesses," said chief executive Graham James.
The firm is in discussion with Amicus GPMS on starting a consultation period.
Colodense prints confectionery and snack food packaging. The site employs 175 staff and houses gravure, flexo and lamination kit.
Work from the Bristol plant will be moved to other Amcor sites in the UK and Western Europe.
As part of the restructure, the firm has also proposed the closure of its plant in Hochheim, Germany.
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