I have recorded a song with all drum arrangements using Logic Pro with the tempo of 85 but when the vocal and along with the arrangement is recorded and played, I feel the vocal tempo is less than the arrangement.How can I rectify this without wasting time in recording the whole project once again.
If the vocals are out of synch with the drums, you can timestretch the vocal track, or chop it into slices and align it with the drums. But this will be a BIG time-waster compared with just re-recording the vocals, getting it right!
But perhaps you mean that the song is together, but just seems a bit slow and lacking in energy? Well, first, reconsider. You're now very familiar with the track. You know exactly what's coming next. To tell the truth you're getting a bit bored with it. But are you SURE speeding it up is the answer? If it is, you can time-stretch the whole mix. Back in the day this would have been done by simply speeding up the tape, shifting pitch as well as tempo. Hence the number of classic recordings that are in unlikely keys, or 'in the crack' between keys.
I think we need more info here as to exactly what's wrong with it...
I think you need to first analyse why the vocal feels out of tempo.
Do you think the song should have been faster in the first place?
Is the vocal just sloppily timed against the track?
Could you fix the track, which might be easier than fixing the vocal?
Did you already attempt to slide one against the other to test if it's just a front- or back-beat issue?
An perhaps more importantly...
Did you record a guide vocal early in the process so you would know if the entire idea even works at all, before blasting ahead with the full arrangement?
You can make some good headway on a track, you can think it's [insert current buzz-word here or just substitute cool] - but if you haven't tested the vocal against it & have something to work against as you construct the final tracking, you don't know if it's a good or bad song until you finished potentially wasting your time on the arrangement. [Cruel, but fair.]
The song is the master.
The arrangement ought to be slave to that.
Even after all that, if you are absolutely certain the song is good...
Rescuing a poor vocal on a good track will take more time & skill & either software, like Melodyne or VocAlign Pro [or please no, AutoTune] or a damn steady hand & a good feel for what is needed with manual tweaks & time-stretches, than getting a better/more sympathetic vocalist who could knock it out in 2 hours.