In most cases, the original basis for your mutual fund shares is simply their cost or purchase price. If there were any commissions or load charges that you paid for the purchase, include those in the basis as well.
If you received your mutual fund shares as a gift, your original basis is generally equal to the donor's adjusted basis at the time of the gift, plus all or part of any gift tax that was paid on the gift, depending on the date of the gift. Special rules apply if, at the time that your donor gave you the shares, their fair market value was less than the donor's adjusted basis.
If you inherited your mutual fund shares, your original basis is generally equal to the fair market value of the shares at the date of death. That means the tax on any appreciation that occurred during the original owner's life is forgiven.