Not all jobs need to be listed on your resume. If you have only been at a job for a month and plan to remain working there for the time being, you should include that job on your resume. However, if you held a job for only a month and you no longer work there, you do not necessarily have to list it on your resume.
List all positions you currently hold, especially if the positions pertain to the job for which you are applying.This is true whether you have been at a job for a month or longer. A potential employer will want to know whether you are currently working when he considers hiring you. If you are doing some work on the side that is not relevant your main line of work, you may omit it from your resume.
If you are working in a temporary position that will end in the near future that is related to your line of work, you can list it on your resume if you think it will enhance your chances of getting another job. You can indicate that the job is temporary and will end at a certain time when you write the dates you have worked at the job.
It is preferable not to list a job that only lasted a month.You probably didn't gain much experience or develop many useful new skills that would benefit you or a future employer. Generally, it is best to only list jobs that you worked at for six months or longer to avoid appearing as though you have difficulty holding down jobs. A period of six months or longer is likely enough time to gain some helpful experience and useful knowledge on the job.
Always list a current position even if you have only been on the job for four weeks. Employers must plan your possible start date if they offer you a position. They also may want to know if you are working at one of their competitors; this is also helpful in considering salary and determining your level of experience and skillset. Being hired for the same position by a competitor may give your abilities more credibility.