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?
Correct answer is: no, you can’t. =(
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”.
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.”