The court said it was upholding its sentencing of ten years and four months for Yuan Hsiao-lung, the former deputy chief of the logistics command, on convictions of bribery, blackmail and leaking secrets.
Yuan was first convicted by a district court in 2009.
In a final ruling, the court rejected an appeal filed by prosecutor-general Huang Shyh-ming on the grounds that the sentence was too heavy since Yuan had confessed and that he did not make any illegal financial gains.
Lin promised to pay Tw$6 million ($200,000) to Yuan to persuade his superiors to promote him to the rank of general, in exchange for information on military contract bidding in 2006.
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But Lin never actually paid the money and Yuan was not promoted before he retired in 2008.
Lin was found to have won several military contracts with Yuan's help, who leaked information on tenders.
The case revived rumours that some military officers were promoted to general through bribery during the 2000-2008 rule of former president Chen Shui-bian.
Two top politicians from the ruling Kuomintang party known for their close ties with incumbent President Ma Ying-jeou have also been indicted on corruption charges since 2012.