Can I improve Google speech API recognition by give him a words list (in my case the request of user is very predictable) to make recognition more accurate?
For Google Cloud Speech API (Not Web Speech API) but some may find this useful:
Although currently in beta, Google has released new capability which allows you to
include a list of phrases to act as "hints" to Cloud Speech-to-Text. Providing these hints, a technique called speech adaptation, helps Speech-to-Text API to recognize the specified phrases from your audio data."
See https://cloud.google.com/speech-to-text/docs/context-strength
I can't speak for Chrome, but in Android they are quite clear that you cannot provide a grammar. In Android speech recognition you are limited to a choice of two models: "free form" and "web search".
See Android: Speech Recognition Append Dictionary?
Correct answer is: no, you can't. =(