I would like to prohibit cloud function from accessing to the Internet(e.g. http request).
It seems that you can achieve it by using Serverless VPC Access connector and "Route all traffic through the VPC connector" settings, but I'm not sure.
I don't have much experience of cloud infrastructure and am a newbie of GCP.
I really appreciate it if you give me any advice.
I read GCP documents. https://cloud.google.com/functions/docs/networking/network-settings?hl=en
You can use a service named "Secure web proxy". It allows you to control the list of authorized URL on the internet. Authorized nothing, you will have access to nothing.
To make it working, you must use a serverless VPC connector on your Cloud Functions, to route your egress traffic to your VPC and then go through the secure web proxy. Set the egress to ALL traffic to route private and public request to the VPC.