Zynga said on Wednesday that it planned to sell additional shares, three months after the social game giant went public, to let some investors trim their holdings.

The company said in a statement that the follow-on offering, which listed a preliminary sales target of $400 million, was meant to “facilitate an orderly distribution of shares and to increase the company’s public float.”

Zynga said in a regulatory filing that it would not receive any proceeds from the sale.

The new offering will come well before the expiration of a 165-day “lock-up” period in which investors won’t be able to sell their holdings. By spacing out additional share sales, Zynga may be aiming to smooth out the huge stock swings that accompany big follow-on offerings.

The offering will also make more of Zynga’s shares available to the public markets. The company sold about 14 percent of its outstanding stock in its initial public offering, on the high side of recent technology I.P.O.’s but low compared with the offerings of more traditional companies.

Shares in Zynga initially traded well after the company’s December I.P.O., but drifted downward. The stock received a huge jolt after Facebook announced its own stock sale plans, and is currently up about 42 percent since it began trading.

The sale will be led by Morgan Stanley and Goldman Sachs, with Bank of America Merrill Lynch, Barclays Capital, JPMorgan Chase and Allen Company listed as additional underwriters.