This paper studies how the subsidy support, e.g. price support and reimbursed investment cost support, affects the investment decision of a monopoly firm under uncertainty and analyzes the implications for social welfare. The analytical results show that the unconditional, i.e., subsidy support that is introduced from the beginning, makes the firm invest earlier. Under a linear demand structure, the unconditional subsidy cannot align the firm's investment decision to the social optimal one. However, a conditional subsidy, i.e., subsidy support introduced at the social optimal investment threshold, can align the two decisions. For a non-linear demand structure, it is possible for the unconditional subsidy to make the firm invest according to the social optimum. When the investment decisions are aligned, the firm's investment leads to the first-best outcome.