Most who believe that tithing is applicable for the New Testament Christian, think this passage refers to a second and third tithe. Since in their mind, the "first tithe" spoke of in Numbers 18 was given to the Levites. Therefore this must be an additional tithe(s).
Deuteronomy 14:22-29
22 Be sure to set aside a tenth of all that your fields produce each year. 23 Eat the tithe of your grain, new wine and olive oil, and the firstborn of your herds and flocks in the presence of the Lord your God at the place he will choose as a dwelling for his Name, so that you may learn to revere the Lord your God always. 24 But if that place is too distant and you have been blessed by the Lord your God and cannot carry your tithe (because the place where the Lord will choose to put his Name is so far away), 25 then exchange your tithe for silver, and take the silver with you and go to the place the Lord your God will choose. 26 Use the silver to buy whatever you like: cattle, sheep, wine or other fermented drink, or anything you wish. Then you and your household shall eat there in the presence of the Lord your God and rejoice. 27 And do not neglect the Levites living in your towns, for they have no allotment or inheritance of their own.
28 At the end of every three years, bring all the tithes of that year’s produce and store it in your towns, 29 so that the Levites (who have no allotment or inheritance of their own) and the foreigners, the fatherless and the widows who live in your towns may come and eat and be satisfied, and so that the Lord your God may bless you in all the work of your hands.
If the Levites were already getting the "first tithe", verses 27 and 29 would make no sense at all. How could you say the Levites have no allotment or inheritance if they were already getting a tithe. No, this must be the one and only tithe. These passages are simply explaining how the tithing system was to work. In other words a further explanation of Numbers 18:21.
Could have some interesting applications for those who believe the Old Testament tithing system is still part of God's will for His children.