Your sentence is fine, Ilham. Home in your example is behaving like an adverb expressing direction. We do not need a preposition with home when it is used with any verb referring to direction:

• I shall be arriving / going / coming / leaving home late this evening.

Note that most verbs expressing direction require the preposition to before the noun, but not home. Compare the following:

• I made my way to the mosque before sunrise.
  
• I ran all the way to the theatre so that I wouldn't be late.
  
• I'm going to walk to work from now on. It's healthier.
  
• I arrived at the harbour just as the boat was leaving.

Once you arrive home, you are then at home and no more direction is suggested, so at is then the appropriate preposition to use with home:

• Will you be at home tonight or are you going out? ~ No, I'll be at home. ~ I'll pop round and see you then.

However, even here, at is often omitted, especially in American English.

No article with common nouns

Note that there are a number of common fixed expressions with prepositions involving everyday time and place nouns where no article is required:

after school / at school / before school / from school /in school to school

after university / at university / to university

in bed / out of bed / to bed

at home / from home / go home / leave home

after work / at work/ before work / from work / to/into work /leave work

from town / in town / out of town/ to/into town

after breakfast* at breakfast* before breakfast* for breakfast* to breakfast*

* OR: lunch, tea, dinner, supper

by bike/car/bus/taxi/tube/train/plane/boat - BUT on foot

• More and more people work from home these days at least one or two days per week.
  
  
• I'm going into town this afternoon. Do you want me to get you anything?
  
  
• I find it difficult to get out of bed, but always exercise for half an hour before breakfast, have fruit juice and muesli for breakfast and then walk to work.
  
  
• At school I studied biology, geography and English, but at university I'm going to study psychology.
  
  
• It's quicker on foot or by bike. It will take you ages to get there if you go by car.

However, if you are referring to a specified breakfast, bed, school, piece of work etc, the definite article will normally be required:

• The bed I slept in last night was most uncomfortable.
  
  
• The lunch you prepared this morning was delicious.
  
  
• I'll meet you outside the school at eight thirty.
  
  
• The work that you did on the Tudors was excellent.
  
  
• The car you sold me for £500 is unreliable.
  

If you would like more practice more please visit our in the You, Me and Us part of our website.