One way to make grape jelly without using pectin is to cook grape pulp on its own, and then stir in the grape skins and sugar until the mixture approaches a jellying point. Other ways of making jelly without pectin include freezing thinner jellies to thicken them or using gelatin.
To make grape jelly without pectin, start by gathering 3 pounds of ripe Concord grapes and 3 cups of sugar. Wash the grapes thoroughly, remove the grapes from their stems, and discard the stems. One at a time, squeeze the grapes out of their skins, collecting the pulp in a large pot. Set aside the skins to use later. Cover the pot of grape pulp, and bring it to a low boil. Stir occasionally, letting the pulp cook for about five minutes. Remove the pot from the stove when the pulp has broken down into a mushy state.
Pour the pulp into a sieve above the pot, and work the pulp through the sieve. Discard the seeds, and return the pot to the stove. Take the grape skins that you have set aside, and add them to the pulp. Bring the mixture to a light boil, and stir for two minutes. The mixture should be dark purple. Add 3 cups of sugar to the pot, one cup at a time, and stir constantly at a rolling boil. When the jelly thickens to the point that it drops heavily off a spoon, the jelly is done. Remove it from the heat, and collect the finished jelly into jars.