The charity pledges never to put down a healthy dog, which means it is committed to often expensive veterinary care for some of the animals it looks after.
To hammer home the message the mailer, which is being sent to warm donors, features images of a beagle called Gabriel, who suffers from arthritis and was found abandoned on Christmas Day.
The campaign comes just after the high-profile case of 204 Yorkshire Terriers were found abandoned in a shed in West Sussex.
The mailer, which is sent out in blue and yellow design, contains messages from Gabriel, who is pictured within a large pair of cupped hands, saying, "will you help me to stay in safe hands" and, "Please help me to get the special care I need".
There are three other real-life stories of dogs who need special care in the mail shot, which has been developed and created by WPP-owned 141 Worldwide/London and launches this month.
Steve Harding, chief executive officer of the agency, said: "This mailer ensures recipients can visualise the dedicated treatment that dogs receive from Dogs Trust and it neatly illustrates exactly what their donation will help to pay for."
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