Despite back-to-back defeats to Chelsea and Arsenal in their last two matches of the year, the Upton Park outfit have made a promising start to the 2014-15 season, currently sitting sixth in the Premier League.
West Ham end 2014 with 56 points for the calendar year and Allardyce wants to see the club register a similar total at the end of the season.
"Fifty-six points in one year is a pretty good record and that would probably finish us in the top eight at least," he said.
"We just need to carry that on and make sure we get 56 this season, or more, because if we can do it one year, let's try and do it in one season and see where it gets us."
West Ham next face West Brom in the Premier League on New Year's Day.
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