Plum trees typically don't bear fruit until they are 3 to 5 years old. Your plum tree might simply be too young to bear fruit. Continue caring for it and it will produce fruit.
Lack of Plums Indicates a Problem
In order to bear fruit, your plum tree must be healthy. Fertilise your tree in the spring as soon as new leaves bud to add nutrients to the soil. Check your tree for insects or fungal infections that may stress it enough to keep it from flowering. Many plum trees need another plum cultivar nearby to cross-pollinate for fruit to develop.
Know what variety of plum you have in order to provide optimal growing, flowering and fruit-producing conditions. Lack of fruit on an immature tree doesn't indicate a problem; however, lack of fruit on an adult tree indicates a problem requiring action.