Forward-secure public-key schemes with untrusted update are a variant of forward-secure public-key schemes such that the private key can be updated in the encrypted version. In this paper, we firstly describe forward-secure public-key scheme with untrusted update and security definition. We put forward a generic construction and prove its security in standard model. In our construction, the forward security is realized by applying a binary tree encryption and the update security is achieved by using a symmetric encryption. Meanwhile, we proved our scheme in the standard model. Our generic construction is very practical compare with previous works.